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On Sequential Optimality Conditions without Constraint Qualifications for Nonlinear Programming with Nonsmooth Convex Objective Functions
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S. Ahmadi   , N. Movahedian |
| Department of Mathematics, University of Isfahan, Isfahan, Iran , s-ahmady@sci.ui.ac.ir |
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Abstract: (26783 Views) |
| 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 constraint qualifications. It is proved that nonsmooth complementary approximate Karush-Kuhn-Tucker conditions are stronger than nonsmooth approximate gradient projection conditions. Sufficiency for differentiable generalized convex programming is established. |
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| Keywords: Optimization problems, Necessary optimality conditions, Constraint qualification, Necessary optimality conditions, Nonsmooth analysis |
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Full-Text [PDF 828 kb]
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Type of Study: Original |
Subject:
Other
Received: 2013/08/25 | Accepted: 2014/09/19 | Published: 2015/09/16
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