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  • Articles  (9)
  • mathematical programming  (3)
  • numerical methods  (3)
  • mathematics  (2)
  • Chebyshev  (1)
  • 2020-2023
  • 2010-2014
  • 1970-1974  (9)
  • 1965-1969
  • Mathematics  (9)
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  • Articles  (9)
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  • 1
    Electronic Resource
    Electronic Resource
    Error estimates of Hermite interpolation (1973)
    Springer
    BIT 13 (1973), S. 338-343 
    Details
    ISSN: 1572-9125
    Keywords: Hermite interpolation ; Chebyshev ; order of continuity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper presents a procedure for obtaining error estimates for Hermite interpolation at the Chebyshev nodes {cos ((2j+1)π/2n)} j =0n−1 −1≦x≦1, for functionsf(x) of various orders of continuity. The procedure is applicable in many cases when the usual Lagrangian error bound is not, and is a better bound, in general, when both are applicable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01951944
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  • 2
    Electronic Resource
    Electronic Resource
    A piecewise exponential model for seismic well-logging data (1974)
    Springer
    Mathematical geology 6 (1974), S. 33-45 
    Details
    ISSN: 1573-8868
    Keywords: inversion of data ; mathematics ; numerical analysis ; regression analysis ; geophysics ; petroleum ; well logging
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Conventional methods of analyzing sonic log data do not always yield accurate information on each velocity segment of a well. It is shown here that the velocity-depth parameters and the sections of approximately constant velocity may be more precisely defined by using an exponential spline to model the data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02111925
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  • 3
    Electronic Resource
    Electronic Resource
    Equations for stress and displacement fields around pressurized elliptical holes in elastic solids (1973)
    Springer
    Mathematical geology 5 (1973), S. 11-25 
    Details
    ISSN: 1573-8868
    Keywords: mathematics ; structural geology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract A mechanical model based upon elasticity theory for the deformation around a pressurized elliptical hole in an homogeneous, isotropic solid has found application in many areas of engineering, rock mechanics, and structural geology. The explicit equations for stress and displacement around such a hole are given. An apl computer program for calculating these stresses and displacements also is presented. These equations and this program should ease future usage of this model by engineers and geologists.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02114084
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  • 4
    Electronic Resource
    Electronic Resource
    On sensitivity in optimal control problems (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 56-73 
    Details
    ISSN: 1573-2878
    Keywords: Sensitivity analysis ; control theory ; mathematical programming ; method of multipliers ; Banach spaces
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two types of interpretations of multipliers in both static and dynamic optimization problems are described. It is snown that the Lagrange multipliers encountered in mathematical programming problems and the auxiliary functions arising in Pontryagintype optimal control problems sometimes have highly analogous interpretations as rates of change of the optimal attainable value of an objective function, or in some cases as bounds on average rates of change.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935609
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  • 5
    Electronic Resource
    Electronic Resource
    A second-order iterative technique for differential-integral systems (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 179-185 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control theory ; functional differential equations ; numerical methods ; hereditary processes ; contraction mapping principle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This note considers the optimal control of a system represented by nonlinear differential-integral equations with a general cost function. A second-order iterative method of solution based on the fixed-point contraction mapping principle is proposed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935538
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  • 6
    Electronic Resource
    Electronic Resource
    Parameter variation for the solution of two-point boundary-value problems and applications in the calculus of variations (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 164-178 
    Details
    ISSN: 1573-2878
    Keywords: Two-point boundary-value problems ; calculus of variations ; numerical methods ; differential equations ; computing methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In the parameter variation method, a scalar parameterk, kε[0, 1], is introduced into the differential equations. The parameterk is inserted in such a way that, whenk=0, the solution of the boundary-value problem is known or readily calculated and, whenk=1, the problem is identical with the original problem. Thus, bydeforming the solution step-by-step throughk-space fromk=0 tok=1, the original problem may be solved. These solutions then provide good starting values for any convergent, iterative scheme such as the Newton-Raphson method. The method is applied to the solution of problems with various types of boundary-value specifications and is further extended to take account of situations arising in the solution of problems from variational calculus (e.g., total elapsed time not specified, optimum control not a simple function of the variables).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00935537
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  • 7
    Electronic Resource
    Electronic Resource
    A mixed integer programming model for scheduling orders in a steel mill (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 305-318 
    Details
    ISSN: 1573-2878
    Keywords: Integer programming ; mathematical programming ; scheduling ; linear programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of scheduling orders at each facility of a large integrated steel mill is considered. Orders are received randomly, and delivery dates are established immediately. Each order is filled by converting raw materials into a finished saleable steel product by a fixed sequence of processes. The application of a deterministic mixed integer linear programming model to the order scheduling problem is given. One important criterion permitted by the model is to process the orders in a sequence which minimizes the total tardiness from promised delivery for all orders; alternative criteria are also possible. Most practical constraints which arise in steelmaking can be considered within the formulation. In particular, sequencing and resource availability constraints are handled easily. The order scheduling model given here contains many variables and constraints, resulting in computational difficulties. A decomposition algorithm is devised for solving the model. The algorithm is a special case of Benders partitioning. Computational experience is reported for a large-scale problem involving scheduling 102 orders through ten facilities over a six-week period. The exact solution to the large-scale problem is compared with schedules determined by several heuristic dispatching rules. The dispatching rules took into consideration such things as due date, processing time, and tardiness penalties. None of the dispatching rules found the optimal solution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932613
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  • 8
    Electronic Resource
    Electronic Resource
    Parametric solution to the joint system identification and optimization problem (1974)
    Springer
    Journal of optimization theory and applications 13 (1974), S. 582-605 
    Details
    ISSN: 1573-2878
    Keywords: System identification ; multicriteria optimization ; mathematical programming ; duality theory ; system modeling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This study is concerned with the simultaneous identification and optimization of static systems. The necessity and the advantages of an integrated approach to the identification and optimization of the system model is established theoretically as well as computationally. A parametric approach to the integrated problem is proven to converge to the integrated problem solution. The general methodology of decomposition of large-scale systems is extended by implementingfeasible decomposition of the joint problem. A multilevel approach is then utilized to successfully solve example problems. Handling the system constraints via a penalty-function technique is shown to be an efficient approach when using the parametric formulation of the joint problem. Numerical results for two example problems are presented using the Univac 1108 digital computer, revealing the economic advantages and disadvantages of the integrated approach to the identification and optimization problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00933046
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  • 9
    Electronic Resource
    Electronic Resource
    Decomposition technique for minimum time trajectories (1974)
    Springer
    Journal of optimization theory and applications 14 (1974), S. 233-250 
    Details
    ISSN: 1573-2878
    Keywords: Time-optimal control ; decomposition methods ; two-point boundary-value problems ; trajectories ; numerical methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A decomposition technique is presented for minimum-time trajectories which are characterized by intermediate constraints and discontinuities. The optimization of such multiple are trajectories is usually a formidable task. One optimization method, trajectory decomposition, breaks the original trajectory at points of discontinuity into separate arcs and then optimizes each are subject to prescribed boundary conditions. This constitutes a first level of control. Each first-level solution is evaluated by a second-level controller, which iteratively specifies new are boundary conditions in order to achieve an optimum solution. Unfortunately, this two-level method cannot be applied directly to minimum-time trajectories. The two-level trajectory decomposition method is extended here to a three-level technique for treating the minimum-time trajectory. The first level again optimizes each are for specified intervention parameters. The new second level, the time interface controller, exploits certain homogeneity properties to satisfy time transversality conditions at all boundaries and to couple the first-level solution arcs in time. The third level, the state interface controller, satisfies state transversality conditions at the arc junctions iteratively while driving the trajectory to its optimum. The new three-level procedure represents a feasible decomposition because each solution trajectory in the iterative sequence is physically realizable. The technique also offers a decentralization of control effort and reduction of initial-value sensitivities. An example problem is formulated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00932942
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