نتایج جستجو برای: constraint qualifications

تعداد نتایج: 82666  

Journal: :Math. Program. 2013
Jane J. Ye Jin Zhang

In this paper we study necessary optimality conditions for nonsmooth optimization problems with equality, inequality and abstract set constraints. We derive the enhanced Fritz John condition which contains some new information even in the smooth case than the classical enhanced Fritz John condition. From this enhanced Fritz John condition we derive the enhanced Karush-Kuhn-Tucker (KKT) conditio...

Journal: :Math. Program. 2013
Stephan Dempe Alain B. Zemkoho

We consider the bilevel programming problem and its optimal value and KKT one level reformulations. The two reformulations are studied in a unified manner and compared in terms of optimal solutions, constraint qualifications and optimality conditions. We also show that any bilevel programming problem where the lower level problem is linear with respect to the lower level variable, is partially ...

2006
N. DINH

This paper provides KKT and saddle point optimality conditions, duality theorems and stability theorems for consistent convex optimization problems posed in locally convex topological vector spaces. The feasible sets of these optimization problems are formed by those elements of a given closed convex set which satisfy a (possibly in…nite) convex system. Moreover, all the involved functions are ...

2014
Helmut Gfrerer Diethard Klatte Michael Jung Sergei V. Nepomnyaschikh Ralf Pfau Joachim Schöberl

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lischitz and upper Hölder type, respectively, hold. Furthermore, we apply the a...

Journal: :Math. Program. 2016
Helmut Gfrerer Diethard Klatte

This paper studies stability aspects of solutions of parametric mathematical programs and generalized equations, respectively, with disjunctive constraints. We present sufficient conditions that, under some constraint qualifications ensuring metric subregularity of the constraint mapping, continuity results of upper Lipschitz and upper Hölder type, respectively, hold. Furthermore, we apply the ...

2007
Jane J. Ye Soon-Yi Wu E. Polak

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

Journal: :J. Optimization Theory and Applications 2011
Stephan Dempe Alain B. Zemkoho

We consider the optimal value reformulation of the bilevel programming problem. It is shown that the Mangasarian-Fromowitz constraint qualification in terms of the basic generalized differentiation constructions of Mordukhovich, which is weaker than the one in terms of Clarke’s nonsmooth tools, fails without any restrictive assumption. Some weakened forms of this constraint qualification are th...

2006
Xin Tao YE Chong LI

The BCQ and the Abadie CQ for infinite systems of convex inequalities in Banach spaces are characterized in terms of the upper semi-continuity of the convex cones generated by the subdifferentials of active convex functions. Some relationships with other constraint qualifications such as the CPLV and the Slate condition are also studied. Applications in best approximation theory are provided.

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