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On Smoothing Exact Penalty Functions for Convex Constrained Optimization
SIAM Journal on Optimization, 1994Summary: A quadratic smoothing approximation to nondifferentiable exact penalty functions for convex constrained optimization is proposed and its properties are established. The smoothing approximation is used as the basis of an algorithm for solving problems with (i) embedded network structures, and (ii) nonlinear minimax problems. Extensive numerical
Mustafa Ç. Pinar, Stavros A. Zenios
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An exact penalty function for nonlinear programming with inequalities
Mathematical Programming, 1973It is shown how, given a nonlinear programming problem with inequality constraints, it is possible to construct an exact penalty function with a local unconstrained minimum at any local minimum of the constrained problem. The unconstrained minimum is sufficiently smooth to permit conventional optimization techniques to be used to locate it.
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Exact penalty functions for generalized Nash problems
2006We propose the use exact penalty functions for the solution of generalized Nash equilibrium problems (GNEPs). We show that by this approach it is possible to reduce the solution of a GNEP to that of a usual Nash problem. This paves the way to the development of numerical methods for the solution of GNEPs.
FACCHINEI, Francisco, PANG J. S. .
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Optimal Control Problems via Exact Penalty Functions
Journal of Global Optimization, 1998The paper deals with the problem how some constrained optimization problems (like, for instance, control problems) can be reduced to unconstrained ones by the method called exact penalization. This method needs that a suitable function (nonsmooth functional in general) describing the constrained set in the form of equality satisfies some conditions on ...
Vladimir F. Demyanov +2 more
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Exact penalty functions in isoperimetric problems
Optimization, 2011It was earlier demonstrated, by the so-called main (or simplest) problem of the Calculus of Variations, that the Theory of Exact Penalties allows one not only to derive fundamental results of the Calculus of Variations but also to construct new direct numerical methods for solving variational problems based on the notions of subgradient and ...
V.F. Demyanov, G.Sh. Tamasyan
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Exact penalty function algorithm with simple updating of the penalty parameter
Journal of Optimization Theory and Applications, 1991See the preview in Zbl 0702.90074.
de O. Pantoja, J. F. A., Mayne, D. Q.
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Exact Penalty Functions for Convex Bilevel Programming Problems
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Liu, G. S., Han, J. Y., Zhang, J. Z.
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Problems Related to Estimating the Coefficients of Exact Penalty Functions
Cybernetics and Systems Analysis, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Laptin, Yu. P., Bardadym, T. O.
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Journal of Global Optimization, 2019
For nonlinear optimization problems with equality, inequality and bound constraints, the authors consider a family of penalty functions and prove that, under suitable assumptions, which include a so-called weakly generalized Mangasarian-Fromovitz constraint qualification, when the penalty parameter is large enough every local optimal solution ...
Qian Liu 0016, Yuqing Xu, Yang Zhou 0018
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For nonlinear optimization problems with equality, inequality and bound constraints, the authors consider a family of penalty functions and prove that, under suitable assumptions, which include a so-called weakly generalized Mangasarian-Fromovitz constraint qualification, when the penalty parameter is large enough every local optimal solution ...
Qian Liu 0016, Yuqing Xu, Yang Zhou 0018
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Exact penalty functions and Lagrange multipliers
Optimization, 1991In this paper we consider a class of nondifferentiable penalty functions associated with a Lipschitz programming problem with an abstract geometric constraint. We analyse the relationship between this class of functions and Kuhn-Tucker type necessary conditions for the programming problem.
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