ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Articles  (16)
  • Data
  • Nonlinear Programming  (16)
  • 1980-1984  (16)
  • Mathematics  (16)
Collection
  • Articles  (16)
  • Data
Source
Keywords
Publisher
Years
Year
Topic
  • 1
    Electronic Resource
    Electronic Resource
    A differential equation approach to nonlinear programming (1980)
    Springer
    Mathematical programming 18 (1980), S. 155-168 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Differential Equation ; Global Solution ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A new method is presented for finding a local optimum of the equality constrained nonlinear programming problem. A nonlinear autonomous system is introduced as the base of the theory instead of usual approaches. The relation between critical points and local optima of the original optimization problem is proved. Asymptotic stability of the critical points is also proved. A numerical algorithm which is capable of finding local optima systematically at the quadratic rate of convergence is developed from a detailed analysis of the nature of trajectories and critical points. Some numerical results are given to show the efficiency of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588311
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    On solving a primal geometric program by partial dual optimization (1981)
    Springer
    Mathematical programming 21 (1981), S. 319-330 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Geometric Programming ; Duality Theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The several published methods for mapping a dual solution estimate to a primal solution estimate in posynomial geometric programming provide no criteria for deciding how much deviation from primal feasibility, or discrepancy between the primal and dual objective function values, should be permitted before the primal solution estimate is accepted by the designer. This paper presents a new and simple dual-to-primal conversion method that uses the cost coefficients to provide a sound economic criterion for determining when to accept a primal solution estimate. The primal solution estimate generated is the exact solution to a modified primal obtained from the given primal by modifying the cost coefficients, with the exponent matrix left unchanged. The method is shown to have desirable properties when coupled with a convergent dual algorithm.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584252
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 3
    Electronic Resource
    Electronic Resource
    On the computational utility of posynomial geometric programming solution methods (1982)
    Springer
    Mathematical programming 22 (1982), S. 163-201 
    Details
    ISSN: 1436-4646
    Keywords: Geometric Programming ; Code Comparisons ; Numerical Testing ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Ten codes or code variants were used to solve the five equivalent posynomial GP problem formulations. Four of these codes were general NLP codes; six were specialized GP codes. A total of forty-two test problems was solved with up to twenty randomly generated starting points per problem. The convex primal formulation is shown to be intrinsically easiest to solve. The general purpose GRG code called OPT appears to be the most efficient code for GP problem solution. The reputed superiority of the specialized GP codes GGP and GPKTC appears to be largely due to the fact that these codes solve the convex primal formulation. The dual approaches are only likely to be competitive for small degree of difficulty, tightly constrained problems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581036
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 4
    Electronic Resource
    Electronic Resource
    An elementary survey of general duality theory in mathematical programming (1981)
    Springer
    Mathematical programming 21 (1981), S. 241-261 
    Details
    ISSN: 1436-4646
    Keywords: Dual problem ; Duality Theory ; Optimality Conditions ; Price Functions ; Nonlinear Programming ; Integer Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We survey some recent developments in duality theory with the idea of explaining and unifying certain basic duality results in both nonlinear and integer programming. The idea of replacing dual variables (prices) by price functions, suggested by Everett and developed by Gould, is coupled with an appropriate dual problem with the consequence that many of the results resemble those used in linear programming. The dual problem adopted has a (traditional) economic interpretation and dual feasibility then provides a simple alternative to concepts such as conjugate functions or subdifferentials used in the study of optimality. In addition we attempt to make precise the relationship between primal, dual and saddlepoint results in both the traditional Lagrangean and the more general duality theories and to see the implications of passing from prices to price functions. Finally, and perhaps surprisingly, it appears that all the standard algorithms terminate by constructing primal and dual feasible solutions of equal value, i.e., by satisfying generalised optimality conditions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01584248
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 5
    Electronic Resource
    Electronic Resource
    A method for globally minimizing concave functions over convex sets (1981)
    Springer
    Mathematical programming 20 (1981), S. 22-32 
    Details
    ISSN: 1436-4646
    Keywords: Concave Programming ; Extreme Point Solutions ; Global Optimization ; Nonconvex Programming ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract A method is described for globally minimizing concave functions over convex sets whose defining constraints may be nonlinear. The algorithm generates linear programs whose solutions minimize the convex envelope of the original function over successively tighter polytopes enclosing the feasible region. The algorithm does not involve cuts of the feasible region, requires only simplex pivot operations and univariate search computations to be performed, allows the objective function to be lower semicontinuous and nonseparable, and is guaranteed to converge to the global solution. Computational aspects of the algorithm are discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589330
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 6
    Electronic Resource
    Electronic Resource
    A globally convergent constrained quasi-Newton method with an augmented lagrangian type penalty function (1982)
    Springer
    Mathematical programming 23 (1982), S. 75-86 
    Details
    ISSN: 1436-4646
    Keywords: Constrained Optimization ; Global Convergence ; Nonlinear Programming ; Penalty Function ; Quasi-Newton Method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The recently proposed quasi-Newton method for constrained optimization has very attractive local convergence properties. To force global convergnce of the method, a descent method which uses Zangwill's penalty function and an exact line search has been proposed by Han. In this paper a new method which adopts a differentiable penalty function and an approximate line is presented. The proposed penalty function has the form of the augmented Lagrangian function. An algorithm for updating parameters which appear in the penalty function is described. Global convergence of the given method is proved.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01583780
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 7
    Electronic Resource
    Electronic Resource
    A smoothing-out technique for min—max optimization (1980)
    Springer
    Mathematical programming 19 (1980), S. 61-77 
    Details
    ISSN: 1436-4646
    Keywords: Optimization ; Nonlinear Programming ; Unconstrained Optimization ; Nondifferentiable Optimization ; Min—Max Problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581628
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 8
    Electronic Resource
    Electronic Resource
    Accelerated convergence for the Powell/Hestenes multiplier method (1980)
    Springer
    Mathematical programming 18 (1980), S. 197-214 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Constrained Optimization ; Augmented Lagrangian Methods ; Multiplier Methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is known that augmented Lagrangian or multiplier methods for solving constrained optimization problems can be interpreted as techniques for maximizing an augmented dual functionD c(λ). For a constantc sufficiently large, by considering maximizing the augmented dual functionD c(λ) with respect toλ, it is shown that the Newton iteration forλ based on maximizingD c(λ) can be decomposed into taking a Powell/Hestenes iteration followed by a Newton-like correction. Superimposed on the original Powell/Hestenes method, a simple acceleration technique is devised to make use of information from the previous iteration. For problems with only one constraint, the acceleration technique is equivalent to replacing the second (Newton-like) part of the decomposition by a finite difference approximation. Numerical results are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588314
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 9
    Electronic Resource
    Electronic Resource
    On optimality conditions for structured families of nonlinear programming problems (1982)
    Springer
    Mathematical programming 22 (1982), S. 82-92 
    Details
    ISSN: 1436-4646
    Keywords: Generic Programming ; Optimality Conditions ; Nonlinear Programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Optimality conditions for families of nonlinear programming problems inR n are studied from a generic point of view. The objective function and some of the constraints are assumed to depend on a parameter, while others are held fixed. Techniques of differential topology are used to show that under suitable conditions, certain strong second-order conditions are necessary for optimality except possibly for parameter values lying in a negligible set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581027
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 10
    Electronic Resource
    Electronic Resource
    Comparative computer results of a new complementary pivot algorithm for solving equality and inequality constrained optimization problems (1980)
    Springer
    Mathematical programming 18 (1980), S. 169-185 
    Details
    ISSN: 1436-4646
    Keywords: Nonlinear Programming ; Equality Constraints ; Fixed Points ; Complementary Pivoting Algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract This paper reports the development of a new algorithm for solving the general constrained optimization problem (that of optimizing an objective function subject to both equality and inequality constraints). The approach is based on the complementary pivoting algorithms which have been developed to solve certain classes of fixed point problems. The specific approach is to use the equality constraints to solve for some variables in terms of the remaining ones thus enabling one to eliminate the equality constraints altogether. The result, under certain circumstances, is an optimization problem which may be transformed into a fixed point problem in such a way that a complementary pivoting code may be used to search for a solution. Seventeen test problems have been solved by this method and the results are compared against those obtained from GRG (Generalized Reduced Gradient method). The results of the tests indicate that the fixed point approach is robust (all 17 problems were solved by this method where as GRG solved 16). As to the computer times, the fixed point code proved to be as fast or faster than GRG on the lower dimensional problems; however, as the dimension increased, the trend reversed and on a 40 dimensional problem GRG was approximately 11 times faster. The conclusion from these tests is that when the dimension of the original problem can be reduced sufficiently by the equality constraints, the fixed point approach appears to be more effective than GRG.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01588312
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...