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  • Articles  (5)
  • nonlinear programming  (5)
  • Ecology
  • crystal structure
  • 1980-1984  (5)
  • 1980  (5)
  • Mathematics  (5)
  • Geosciences
  • 1
    Electronic Resource
    Electronic Resource
    A globally convergent, implementable multiplier method with automatic penalty limitation (1980)
    Springer
    Applied mathematics & optimization 6 (1980), S. 335-360 
    Details
    ISSN: 1432-0606
    Keywords: nonlinear programming ; multiplier methods ; penalty methods ; global convergence ; penalty limitation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01442901
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  • 2
    Electronic Resource
    Electronic Resource
    Linearized ridge-path method for function minimization (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 161-179 
    Details
    ISSN: 1573-2878
    Keywords: Optimization techniques ; nonlinear programming ; direct methods ; numerical methods ; conjugate directions ; nongradient methods ; ridge-path methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934494
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  • 3
    Electronic Resource
    Electronic Resource
    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
    Keywords: Least-square methods ; variable-metric methods ; Levenberg-Marquardt methods ; nonlinear programming ; testing algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934786
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  • 4
    Electronic Resource
    Electronic Resource
    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
    Keywords: Nash-equilibrium solutions ; partially controllable strategies ; nonlinear programming ; complementary eigenvalue problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01262978
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  • 5
    Electronic Resource
    Electronic Resource
    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
    Keywords: Generalized convexity ; global minimality ; nonlinear programming ; nonconvex programming ; optimization theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934030
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