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AN ABADIE-TYPE CONSTRAINT QUALIFICATION FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

by Michael L. Flegel, Christian Kanzow , 2002
"... Abstract. Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched in the pa ..."
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Abstract. Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched

ON THE GUIGNARD CONSTRAINT QUALIFICATION FOR MATHEMATICAL PROGRAMS WITH EQUILIBRIUM CONSTRAINTS

by Michael L. Flegel, Christian Kanzow , 2004
"... Abstract. We recapitulate the well known fact that most of the standard constraint qual-i cations are violated for mathematical programs with equilibrium constraints (MPECs). We go on to show that the Abadie constraint qualication is only satised in fairly restric-tive circumstances. In order to avo ..."
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Abstract. We recapitulate the well known fact that most of the standard constraint qual-i cations are violated for mathematical programs with equilibrium constraints (MPECs). We go on to show that the Abadie constraint qualication is only satised in fairly restric-tive circumstances. In order

Constraint qualifications and necessary optimality conditions for optimization problems with variational inequality constraints

by J. J. Ye - SIAM J. OPTIM , 2000
"... A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications for ..."
Abstract - Cited by 30 (15 self) - Add to MetaCart
A very general optimization problem with a variational inequality constraint, inequality constraints, and an abstract constraint are studied. Fritz John type and Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are derived. Several constraint qualifications

Constraint Qualifications for Semi-Infinite Systems of Convex Inequalities

by Wu Li, Chandal Nahak, Ivan Singer , 2000
"... We introduce and study the Abadie constraint qualication, the weak Pshenichnyi-LevinValadier property and related constraint qualications for semi-innite systems of convex inequalities and linear inequalities. Our main results are new characterizations of various constraint qualications in terms of ..."
Abstract - Cited by 19 (1 self) - Add to MetaCart
We introduce and study the Abadie constraint qualication, the weak Pshenichnyi-LevinValadier property and related constraint qualications for semi-innite systems of convex inequalities and linear inequalities. Our main results are new characterizations of various constraint qualications in terms

On constraint qualification for infinite system of convex inequalities in a Banach space

by Chong Li, K. F. Ng - SIAM J. Optim
"... Abstract. For a general infinite system of convex inequalities in a Banach space, we study the basic constraint qualification and its relationship with other fundamental concepts, including various versions of conditions of Slater type, the Mangasarian–Fromovitz constraint qualification, as well as ..."
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Abstract. For a general infinite system of convex inequalities in a Banach space, we study the basic constraint qualification and its relationship with other fundamental concepts, including various versions of conditions of Slater type, the Mangasarian–Fromovitz constraint qualification, as well

NEWTON-TYPE METHODS FOR OPTIMIZATION PROBLEMS WITHOUT CONSTRAINT QUALIFICATIONS

by A. F. Izmailov, M. V. Solodov - SIAM J. OPTIMIZATION , 2004
"... We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification, but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular-value d ..."
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We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification, but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular

Constraint qualifications and KKT conditions for bilevel programming problems

by Jane J. Ye - Math. Oper. Res
"... doi 10.1287/moor.1060.0219 ..."
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doi 10.1287/moor.1060.0219

Generalized Linear Programming Without Constraint Qualifications

by Massachttusetts Institu, Elie Gugenheim, Jeremy F. Shapiro, Elie Gugenheim, Jeremy Shapiro
"... In an earlier paper [2], the equivalence was established between convexi-fication and dualization of an arbitrary mathematical programming problem. Generalized linear programming (also known as Dantzig-Wolfe decomposition) applied to such a problem was shown to be a mechanization of this result in ..."
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In an earlier paper [2], the equivalence was established between convexi-fication and dualization of an arbitrary mathematical programming problem. Generalized linear programming (also known as Dantzig-Wolfe decomposition) applied to such a problem was shown to be a mechanization of this result in

A practical optimality condition without constraint qualifications

by Jose Mario, Fux Svaiter , 2002
"... for nonlinear programming ..."
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for nonlinear programming

Constraint qualification, the strong CHIP, and best approximation with convex constraints in Banach spaces

by Chong Li, K. F. Ng - SIAM J. Optim
"... Abstract. Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily finite ..."
Abstract - Cited by 13 (9 self) - Add to MetaCart
Abstract. Several fundamental concepts such as the basic constraint qualification (BCQ), the strong conical hull intersection property (CHIP), and the perturbations for convex systems of inequalities in Banach spaces (over R or C) are extended and studied; here the systems are not necessarily
Results 11 - 20 of 468