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Constraint Qualifications for Nonsmooth Mathematical Programs with Equilibrium Constraints
Set-Valued and Variational Analysis, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Movahedian, N., Nobakhtian, S.
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Notes on Some Constraint Qualifications for Mathematical Programs with Equilibrium Constraints
Journal of Optimization Theory and Applications, 2012From the introduction: ``Mathematical program with equilibrium constraints (MPEC) plays an important role in many fields such as engineering design, economic equilibria, transportation science, multilevel game, and mathematical programming itself. However, this kind of problems is generally difficult to deal with because their constraints fail to ...
Lei Guo, Gui-Hua Lin
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A class of constraint qualifications in nonsmooth optimization
Annals of Operations Research, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guohui Tian, Xiaofeng Li, Tianxia Zhao
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Geometry of optimality conditions and constraint qualifications
Mathematical Programming, 1972Certain types of necessary optimality conditions for mathematical programming problems are equivalent to corresponding regularity conditions on the constraint set. For any problem, a certain natural optimality condition, dependent upon the particular constraint set, is always satisfied.
Floyd J. Gould, Jon W. Tolle
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General constraint qualifications in nondifferentiable programming
Mathematical Programming, 1990A general inequality-constrained minimization program is considered on a real normed space E. The constraints are given by a finite number of inequalities and an explicit set C. The paper deals with necessary conditions of Kuhn-Tucker type for a local minimum.
R. R. Merkovsky, D. E. Ward
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Characterizations of the Strong Basic Constraint Qualifications
Mathematics of Operations Research, 2005In this paper, we characterize the general difference between strong basic constraint qualification (BCQ) and BCQ. For this purpose, we introduce a new measurement, the extent of a subdifferential, and show that for an inequality defined by a proper convex function f, the strong BCQ at a boundary point x of the solution set is equivalent to the ...
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A simple constraint qualification in convex programming
Mathematical Programming, 1993The authors introduce a rather large class of differentiable convex functions for which the constraint qualifications is always satisfied. Hence, for programs with the constraints belonging to this class, consistency of the Karush-Kuhn-Tucker condition (as a system) is both necessary and sufficient for optimality.
X. Zhou +2 more
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On Constraint Qualifications in Nonsmooth Optimization
Journal of Optimization Theory and Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Avoiding a Constraint Qualification
Optimization, 1997Necessary conditions are given for a constrained minimum, which do not assume any constraint qualification. The conditions relate to a cone, depending on constraint gradients at points near the minimum. They generalize a sufficient condition due to Hanson Under an invexity hypothesis.
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A Cone-Continuity Constraint Qualification and Algorithmic Consequences
SIAM Journal on Optimization, 2016Summary: Every local minimizer of a smooth constrained optimization problem satisfies the sequential approximate Karush-Kuhn-Tucker (AKKT) condition. This optimality condition is used to define the stopping criteria of many practical nonlinear programming algorithms.
Roberto Andreani +3 more
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