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  • 1
    Digitale Medien
    Digitale Medien
    Conjugate direction methods with variable storage (1982)
    Springer
    Mathematical programming 23 (1982), S. 326-340 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; Quasi-Newton ; Conjugate Gradient
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we study conjugate gradient algorithms for large optimization problems. These methods accelerate (or precondition) the conjugate gradient method by means of quasi-Newton matrices, and are designed to utilize a variable amount of storage, depending on how much information is retained in the quasi-Newton matrices. We are concerned with the behaviour of such methods on the underlying quadratic model, and in particular, with finite termination properties.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01583797
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  • 2
    Digitale Medien
    Digitale Medien
    A smoothing-out technique for min—max optimization (1980)
    Springer
    Mathematical programming 19 (1980), S. 61-77 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; Nonlinear Programming ; Unconstrained Optimization ; Nondifferentiable Optimization ; Min—Max Problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR n . Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01581628
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  • 3
    Digitale Medien
    Digitale Medien
    A globally convergent, implementable multiplier method with automatic penalty limitation (1980)
    Springer
    Applied mathematics & optimization 6 (1980), S. 335-360 
    Details
    ISSN: 1432-0606
    Schlagwort(e): nonlinear programming ; multiplier methods ; penalty methods ; global convergence ; penalty limitation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper deals with penalty function and multiplier methods for the solution of constrained nonconvex nonlinear programming problems. Starting from an idea introduced several years ago by Polak, we develop a class of implementable methods which, under suitable assumptions, produce a sequence of points converging to a strong local minimum for the problem, regardless of the location of the initial guess. In addition, for sequential minimization type multiplier methods, we make use of a rate of convergence result due to Bertsekas and Polyak, to develop a test for limiting the growth of the penalty parameter and thereby prevent ill-conditioning in the resulting sequence of unconstrained optimization problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01442901
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  • 4
    Digitale Medien
    Digitale Medien
    Analysis of a sterile insect release model with predation (1982)
    Springer
    Journal of mathematical biology 16 (1982), S. 33-48 
    Details
    ISSN: 1432-1416
    Schlagwort(e): Sterile insect release ; Predation ; Stability ; Limit cycles ; Optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Biologie , Mathematik
    Notizen: Abstract A model for the sterile insect release method of pest control in which the target species is under predatory or parasitic regulation is analyzed. The equations are nondimensionalized and the rescaled parameters are interpreted. There are four types of equilibria, whose existence and stability depend on which of ten regions of parameter space contain the rescaled parameters, and in turn give minimal release rates to achieve eradication of the pest. In at least one region, Hopf bifurcation theory shows the existence of limit cycles, but they are found to be unstable. In addition, the optimal release rate to minimize a total cost functional for pest control by the sterile release method is studied. Both approaches show that when predation accounts for a large fraction of the natural deaths, the necessary release rate and total cost are higher than for weak predation. If the predators are removed without being replaced by any other source of mortality, the cost rises in all cases but rises much more dramatically for cases with strong predation. A definite danger of the sterile release method when some predatory control exists is that the predators are frequently driven extinct before the prey, so that the target species could explode to much higher levels and be more difficult to eradicate again after the sterile release is terminated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00275159
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  • 5
    Digitale Medien
    Digitale Medien
    A new augmented Lagrangian function for inequality constraints in nonlinear programming problems (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 495-519 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; nonlinear programming ; Numerical methods ; computational methods ; augmented Lagrangian functions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, a new augmented Lagrangian function is introduced for solving nonlinear programming problems with inequality constraints. The relevant feature of the proposed approach is that, under suitable assumptions, it enables one to obtain the solution of the constrained problem by a single unconstrained minimization of a continuously differentiable function, so that standard unconstrained minimization techniques can be employed. Numerical examples are reported.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940544
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  • 6
    Digitale Medien
    Digitale Medien
    Equivalence theorem for constrained optimization of the LegendreK-transform of a concave function (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 25-31 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; Kuhn-Tucker theorem ; LegendreK-transform ; equilibrium composition
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The most common way of determining the steady states of a system is through the optimization of a concave function on a convex set. This applies only to cases where the objective function depends exclusively onextensive variables. In fields such as econometrics, physics, or chemistry, controllable quantities (and therefore constrained variables) are generally referred to asintensive parameters, and the states are described through a potential function. In the following pages, we examine how these two aspects can be connected.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934320
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  • 7
    Digitale Medien
    Digitale Medien
    Sufficient conditions for the optimal control of a class systems with continuous lags (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 153-154 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; maximum principle ; sufficient conditions ; integro-differential equations ; path constraints ; economic applications
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Notational errors in Theorem 5.2 of Ref. 1 are corrected.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934332
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  • 8
    Digitale Medien
    Digitale Medien
    An approach to the solution of the vector optimization problem of dynamic systems (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 409-422 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; scalar optimization ; vector optimization ; optimization under vector-valued criteria ; maximum principle ; dynamic programming ; optimization of dynamic systems ; multi-criteria decision problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935346
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  • 9
    Digitale Medien
    Digitale Medien
    On the optimal control problem of a single-server queueing system (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 317-325 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; queueing theory ; phase type distributions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a single-server queueing system (with a finite waiting room) with phase type arrivals and exponential service times, an optimal control for the service rate is derived. This generalizes the result of Scott and Jefferson for theM/M/1/1 queueing model.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935227
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  • 10
    Digitale Medien
    Digitale Medien
    Near-optimum design of nonstationary linear systems with state and control delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 73-88 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; suboptimal control ; time-delay systems ; linear systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A computationally efficient method based on a sensitivity approach is developed to obtain suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. The proposed suboptimal control includes some truncated series whose terms are calculated in a recursive manner from nondelay system optimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934590
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  • 11
    Digitale Medien
    Digitale Medien
    Linearized ridge-path method for function minimization (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 161-179 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization techniques ; nonlinear programming ; direct methods ; numerical methods ; conjugate directions ; nongradient methods ; ridge-path methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A modification based on a linearization of a ridge-path optimization method is presented. The linearized ridge-path method is a nongradient, conjugate direction method which converges quadratically in half the number of search directions required for Powell's method of conjugate directions. The ridge-path method and its modification are compared with some basic algorithms, namely, univariate method, steepest descent method, Powell's conjugate direction method, conjugate gradient method, and variable-metric method. The assessment indicates that the ridge-path method, with modifications, could present a promising technique for optimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934494
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  • 12
    Digitale Medien
    Digitale Medien
    Suboptimal control of systems with multiple delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 621-633 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; time-delay systems ; linear systems ; multiple-delay systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The application of Pontryagin's maximum principle to the optimization of linear systems with time delays results in a system of coupled two-point boundary-value problems involving both delay and advance terms. The exact solution of this system of TPBV problems is extremely difficult, if not impossible. In this paper, a fast-converging iterative approach is developed for obtaining the suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. At each step of the proposed method, a linear nondelay system with an extra perturbing input must be optimized. The procedure can be extended for the optimization of nonlinear systems with multiple time-varying delays, provided that some of the nonlinearities satisfy the Lipschitz condition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01686725
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  • 13
    Digitale Medien
    Digitale Medien
    Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 643-661 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01686727
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  • 14
    Digitale Medien
    Digitale Medien
    Computational experience with Davidon's least-square algorithm (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 27-39 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Least-square methods ; variable-metric methods ; Levenberg-Marquardt methods ; nonlinear programming ; testing algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Computational results are presented for Davidon's new least-square algorithm. Computational experience with this algorithm is reported which motivated the development of a production code version of the algorithm. Several heuristic modifications, which have been added, are described. Fifteen zero-residual test problems have been used in comparing the new production code version with two established versions of the Levenberg-Marquardt algorithm. The production code version of Davidon's least-square algorithm performed faster and used less function evaluations than the Levenberg-Marquardt algorithm in almost every case of the test problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934786
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  • 15
    Digitale Medien
    Digitale Medien
    Junction phenomena for optimal control with state-variable inequality constraints of third order (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 85-99 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; junction conditions ; calculus of variations ; inequality constraints
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is known that extremal arcs governed by inequality constraints of third order (constraint relations that must be differentiated three times to generate a control equation) cannot join an unconstrained arc, except in special cases. But a control problem is exhibited, for which every extremal includes a constrained arc of third order. The constrained arc joins the end of an infinite sequence of consecutive unconstrained arcs of finite total duration. Evidence (but not proof) is given that this phenomenon is typical, rather than exceptional. An analogous phenomenon is well known for optimal control problems with singular arcs of second order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934790
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  • 16
    Digitale Medien
    Digitale Medien
    Constrained nonzero-sum games with partially controllable strategies (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 361-371 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Nash-equilibrium solutions ; partially controllable strategies ; nonlinear programming ; complementary eigenvalue problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The present paper deals with a class of nonzero-sum, two-person games with finite strategies when there are constraints on the strategies selected by the players. The constraints arise due to the subjective difficulty that each player often has in assigning to the states probabilities with which he is completely satisfied, and the model specifies how much each player must perturb his initial probability estimate in order to change his maximum utility alternative from the alternative originally best under the initial estimate. It is shown that the Nash-equilibrium solution of this class of nonzero-sum games can be characterized by an equivalent nonlinear program which leads in some cases to a pair of complementary eigenvalue problems. Applications to normal or approximate solutions of linear programming problems are also indicated.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01262978
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  • 17
    Digitale Medien
    Digitale Medien
    Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 515-533 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934475
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  • 18
    Digitale Medien
    Digitale Medien
    On optimal control problems with state constraints (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 75-80 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; state constraints ; multipliers ; perturbation theory
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper is concerned with necessary conditions for a general optimal control problem developed by Russak and Tan. It is shown that, in most cases, a further relation between the multipliers holds. This result is of interest in particular for the investigation of perturbations of the state constraint.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934843
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  • 19
    Digitale Medien
    Digitale Medien
    A property of an autonomous minimax optimal control problem (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 81-87 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; minimax problems ; maximum principle ; Hamiltonian function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A control system $$\dot x = f\left( {x,u} \right)$$ ,u) with cost functional $$\mathop {ess \sup }\limits_{T0 \leqslant t \leqslant T1} G\left( {x\left( t \right),u\left( t \right)} \right)$$ is considered. For an optimal pair $$\left( {\bar x\left( \cdot \right),\bar u\left( \cdot \right)} \right)$$ ,ū(·)), there is a maximum principle of the form $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right) = \mathop {\max }\limits_{u \in \Omega \left( t \right)} \eta \left( t \right)f\left( {\bar x\left( t \right),u} \right).$$ By means of this fact, it is shown that $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right)$$ is equal to a constant almost everywhere.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934844
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  • 20
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    Digitale Medien
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934725
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  • 21
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    Digitale Medien
    Sufficient conditions for asymptotic optimal control (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 307-325 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; asymptotic optimal control ; calculus of variations ; Lagrange problems ; global minima ; absolute minima ; necessary conditions ; sufficient conditions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For a selected family of Lagrange-type control problems involving a nonnegative integral costJ T (y,u) over the interval [0,T], 0〈T〈∞, with system conditions consisting of differential inequalities and/or equalities, the following material is treated: (i) a resumé of relevant necessary conditions and sufficient conditions for a pair (y T ,u T ) to minimizeJ T (y,u); (ii) conditions sufficient for the convergence asT→∞ of minimizing pairs (y T ,u T ) over [0,T] to a limit pair (y ∞,u ∞) over the infinite-time interval [0, ∞); (iii) conditions sufficient for (y ∞,u ∞) to minimize the costJ ∞(y,u) over [0, ∞); and (iv) conditions sufficient for the optimal cost per unit timeJ T (y T ,u T )/T to have a limit asT→∞.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934555
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  • 22
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    Digitale Medien
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934557
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  • 23
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    Digitale Medien
    System theory: A new approach to wave mechanics (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 463-478 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; control ; relativity ; stochastic processes ; wave mechanics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The intention of this paper is to show how the influence of the work of Bellman has initiated a tentative new approach to quantum mechanics
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934034
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  • 24
    Digitale Medien
    Digitale Medien
    Generalized arcwise-connected functions and characterizations of local-global minimum properties (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 407-425 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Generalized convexity ; global minimality ; nonlinear programming ; nonconvex programming ; optimization theorems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, new classes of generalized convex functions are introduced, extending the concepts of quasi-convexity, pseudoconvexity, and their associate subclasses. Functions belonging to these classes satisfy certain local-global minimum properties. Conversely, it is shown that, under some mild regularity conditions, functions for which the local-global minimum properties hold must belong to one of the classes of functions introduced.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934030
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  • 25
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    Digitale Medien
    On the order of singular optimal control problems (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 479-489 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; singular control ; junction conditions ; singular control order
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934035
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  • 26
    Digitale Medien
    Digitale Medien
    On the general inverse problem of optimal control theory (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 491-497 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; inverse problems ; dynamic programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The general inverse problem of optimal control is considered from a dynamic programming point of view. Necessary and sufficient conditions are developed which two integral criteria must satisfy if they are to yield the same optimal feedback law, the dynamics being fixed. Specializing to the linear-quadratic case, it is shown how the general results given here recapture previously obtained results for quadratic criteria with linear dynamics.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934036
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  • 27
    Digitale Medien
    Digitale Medien
    Shape design sensitivity of a membrane (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 595-623 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; partial differential equations ; elasticity ; control ; design sensitivity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The dependence of the static response and the eigenvalues of a membrane on its shape is characterized. A transformation function is defined to determine the shape of the membrane. Differential operator properties and transformation techniques of integral calculus are employed to show that the static response and the eigenvalues of the system depend in a continuous and differentiable way on the shape of the membrane. Explicit and computable formulas are presented for the derivative (first variation) of the structural response and the eigenvalues with respect to the shape. A rigorous proof is provided, and the shape design sensitivity of a typical integral functional is determined.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933973
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  • 28
    Digitale Medien
    Digitale Medien
    Sensitivity analysis in geometric programming (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 1-21 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Sensitivity analysis ; geometric programming ; nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A unified approach to computing first, second, or higher-order derivatives of any of the primal and dual variables or multipliers of a geometric programming problem, with respect to any of the problem parameters (term coefficients, exponents, and constraint right-hand sides) is presented. Conditions under which the sensitivity equations possess a unique solution are developed, and ranging results are also derived. The analysis for approximating second and higher-order sensitivity generalizes to any sufficiently smooth nonlinear program.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934363
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  • 29
    Digitale Medien
    Digitale Medien
    Additional necessary conditions for optimal control with state-variable inequality constraints (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 241-250 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; state constraints ; necessary conditions for optimality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is shown that, when the set of necessary conditions for an optimal control problem with state-variable inequality constraints given by Bryson, Denham, and Dreyfus is appropriately augmented, it is equivalent to the (different) set of conditions given by Jacobson, Lele, and Speyer. Relationships among the various multipliers are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934086
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  • 30
    Digitale Medien
    Digitale Medien
    Global optimization by controlled random search (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 333-348 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Numerical optimization ; global search ; nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The paper describes a new version, known as CRS2, of the author's controlled random search procedure for global optimization (CRS). The new procedure is simpler and requires less computer storage than the original version, yet it has a comparable performance. The results of comparative trials of the two procedures, using a set of standard test problems, are given. These test problems are examples of unconstrained optimization. The controlled random search procedure can also be effective in the presence of constraints. The technique of constrained optimization using CRS is illustrated by means of examples taken from the field of electrical engineering.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933504
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  • 31
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    Digitale Medien
    Multiplier rules and the separation of convex sets (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 321-331 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; necessary conditions ; Kuhn-Tucker theorem ; multiplier rules ; separation of convex sets ; mathematical programming ; generalized derivatives
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider the following abstract mathematical programming problem: in a setD, find an element that optimizes a real function φ0, subject to inequality constraints φ1⩽0, ..., φ p ⩽0 and equality constraints φ p+1=0, ..., φ p+q =0. Necessary conditions for this problem, like the Karush-Kuhn-Tucker theorem, can be seen as a consequence of separating with a hyperplane two convex sets inR p+q+1, the image space of the map Φ=(φ0, φ1, ..., φ p+q ). This paper reviews this approach and organizes it into a coherent way of looking at necessary conditions in optimization theory.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933503
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  • 32
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    Digitale Medien
    Second-order necessary conditions in optimal control: Accessory-problem results without normality conditions (1983)
    Springer
    Journal of optimization theory and applications 41 (1983), S. 75-106 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; second-order necessary conditions ; accessory problem ; control constraints ; normality condition
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract An optimal control problem, which includes restrictions on the controls and equality/inequality constraints on the terminal states, is formulated. Second-order necessary conditions of the accessory-problem type are obtained in the absence of normality conditions. It is shown that the necessary conditions generalize and simplify prior results due to Hestenes (Ref. 5) and Warga (Refs. 6 and 7).
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934437
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  • 33
    Digitale Medien
    Digitale Medien
    A compact updating formula for quasi-Newton minimization algorithms (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 477-494 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Unconstrained optimization ; variable-metric methods ; quasi-Newton methods ; numerical algorithms ; nonlinear programming
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Quasi-Newton algorithms minimize a functionF(x),x ∈R n, searching at any iterationk along the directions k=−H kgk, whereg k=∇F(x k) andH k approximates in some sense the inverse Hessian ofF(x) atx k. When the matrixH is updated according to the formulas in Broyden's family and when an exact line search is performed at any iteration, a compact algorithm (free from the Broyden's family parameter) can be conceived in terms of the followingn ×n matrix: $$H{_R} = H - Hgg{^T} H/g{^T} Hg,$$ which can be viewed as an approximating reduced inverse Hessian. In this paper, a new algorithm is proposed which uses at any iteration an (n−1)×(n−1) matrixK related toH R by $$H_R = Q\left[ {\begin{array}{*{20}c} 0 & 0 \\ 0 & K \\ \end{array} } \right]Q$$ whereQ is a suitable orthogonaln×n matrix. The updating formula in terms of the matrixK incorporated in this algorithm is only moderately more complicated than the standard updating formulas for variable-metric methods, but, at the same time, it updates at any iteration a positive definite matrixK, instead of a singular matrixH R. Other than the compactness with respect to the algorithms with updating formulas in Broyden's class, a further noticeable feature of the reduced Hessian algorithm is that the downhill condition can be stated in a simple way, and thus efficient line searches may be implemented.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940543
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  • 34
    Digitale Medien
    Digitale Medien
    On the convergence, invariance, and related aspects of a modification of Huang's algorithm (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 315-341 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; unconstrained minimization ; updates ; line searches ; convergence ; numerical methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a certain generalization of the Huang family of updates and discuss, firstly, convergence, dependence on parameters, and descent property; secondly, invariance under nonlinear scaling, conjugacy of search directions, and possibility of achieving a better approximation of the inverse of the Hessian. The last three aspects are shown to be dependent on particular choices of parameters. A numerical experiment is presented comparing the performances of the usual and modified BFGS algorithms.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935273
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  • 35
    Digitale Medien
    Digitale Medien
    Dynamic programming using singular perturbations (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 221-230 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; dynamic programming ; singular perturbations ; system order reduction
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The singular perturbation method is used in dynamic programming to reduce the order and the computational requirements of linear systems composed of slow and fast modes. After the fast modes are separated, a near-optimum solution is computed at two different iteration rates determined by the slow and fast subsystem dynamics. The result is a reduction in the order of the computational requirement of the given system to that of the slow subsystem.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934084
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  • 36
    Digitale Medien
    Digitale Medien
    Optimal control of two interconnected turbogenerators (1983)
    Springer
    Journal of optimization theory and applications 40 (1983), S. 255-291 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal control ; two interconnected turbogenerators ; torque control ; voltage control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, the optimal control of a system with two identical interconnected turbogenerators, which are connected to an infinite bus, is considered. Control of the generators is effected through control of field voltages and turbine torques. The alternators are controlled through a linear feedback of the state variables. The feedback parameters are obtained by solving a nonlinear, two-point boundary-value problem. The values obtained for these parameters depend on the strength and duration of the disturbance, since the model is nonlinear, in contrast to the usual feedback control of a linear model. The numerical values used are indicated in the Appendix.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00933940
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