Constraint Qualifications for Convex Inequality Systems with Applications in Constrained Optimization
نویسندگان
چکیده
منابع مشابه
Constraint Qualifications for Convex Inequality Systems with Applications in Constrained Optimization
For an inequality system defined by an infinite family of proper convex functions, we introduce some new notions of constraint qualifications in terms of the epigraphs of the conjugates of these functions and study relationships between these new constraint qualifications and other wellknown constraint qualifications including the basic constraint qualification studied by Hiriart-Urrutty and Le...
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Sequential optimality conditions for constrained optimization are necessarily satisfied by local minimizers, independently of the fulfillment of constraint qualifications. These conditions support the employment of different stopping criteria for practical optimization algorithms. On the other hand, when an appropriate strict constraint qualification associated with some sequential optimality c...
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Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...
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One revisits the standard saddle-point method based on conjugate duality for solving convex minimization problems. Our aim is to reduce or remove unnecessary topological restrictions on the constraint set. Dual equalities and characterizations of the minimizers are obtained with weak or without constraint qualifications. The main idea is to work with intrinsic topologies which reflect some geom...
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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 the Kuhn–Tucker type necessary optimality conditions involving Mordukhovich coderivatives are intr...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 2008
ISSN: 1052-6234,1095-7189
DOI: 10.1137/060676982