Journal ArticleDOI
Exact penalization via dini and hadamard conditional derivatives
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In this paper, the exact penalty functions for nonsmooth constrained optimization problems are analyzed using the notion of (Dini) Hadamard directional derivative with respect to the constraint set.Abstract:
Exact penalty functions for nonsmooth constrained optimization problems are analyzed tfy using the notion of (Dini) Hadamard directional derivative with respect to the constraint set. Weak conditions are given guaranteeing equivalence of the sets of stationary, global minimum, local minimum points of the constrained problem and of the penalty functionread more
Citations
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Book ChapterDOI
Exact penalty functions for generalized Nash problems
TL;DR: In this article, the authors proposed the use of exact penalty functions for the solution of generalized Nash equilibrium problems (GNEPs) and showed that by this approach, it is possible to reduce the solution to that of a usual Nash problem.
Book ChapterDOI
Exhausters and Convexificators — New Tools in Nonsmooth Analysis
TL;DR: In this paper, positive homogeneous functions play an outstanding role in Nonsmooth Analysis (NSA) and Nondifferentiable Optimization (NDO), since optimality conditions are usually expressed in terms of directional derivatives or their generalizations (the Dini and Hadamard upper and lower directional derivatives, the Clarke derivative, the MichelPenot derivative etc.).
Journal ArticleDOI
VI-constrained hemivariational inequalities: distributed algorithms and power control in ad-hoc networks
TL;DR: The algorithms developed are used to solve a new power control problem in ad-hoc networks that involves the penalization of the non-VI constraint and a combination of proximal and Tikhonov regularization to handle the lower-level VI constraints.
Journal ArticleDOI
A unifying theory of exactness of linear penalty functions
TL;DR: In this article, a theory of exact linear penalty functions is developed, which generalizes and unifies most of the results on exact penalization existing in the literature, and obtain various necessary and sufficient conditions for the exactness of a linear penalty function.
Journal ArticleDOI
Exact penalty functions and calmness for mathematical programming under nonlinear perturbations
TL;DR: In this article, the effects of nonlinear perturbations of constraint systems are considered over the relationship between calmness and exact penalization, within the context of mathematical programming with equilibrium constraints.
References
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Journal ArticleDOI
Non-Linear Programming Via Penalty Functions
TL;DR: The algorithm presented in this paper solves the non-linear programming problem by transforming it into a sequence of unconstrained maximization problems and is shown to be a dual feasible method.
Journal ArticleDOI
Exact penalty functions in constrained optimization
G. Di Pillo,Luigi Grippo +1 more
TL;DR: Formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated, thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions.
Journal ArticleDOI
An Exact Potential Method for Constrained Maxima
TL;DR: In this article, it was shown that the local conditional maximum of the function f on the set is identical with the unconditional maximum of potential function p(x,\mu ) under certain natural assumptions.
Journal ArticleDOI
Necessary and sufficient conditions for isolated local minima of nonsmooth functions
TL;DR: In this paper, the authors considered the mathematical programming problem of finding a subset of a finite-dimensional space where f is an extended real-valued function, and C is an arbitrary subset of the space, and gave necessary and sufficient optimality conditions.
Book ChapterDOI
Exact Penalty Methods
TL;DR: It is shown that, by making use of continuously differentiable functions that possess exactness properties, it is possible to define implementable algorithms that are globally convergent with superlinear convergence rate towards KKT points of the constrained problem.