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A cone-continuity constraint qualification and algorithmic consequences

Roberto Andreani(andreani***at***ime.unicamp.br)
Jose Mario Martinez(martinez***at***ime.unicamp.br)
Alberto Ramos(aramos27***at***gmail.com)
Paulo J. S. Silva(pjssilva***at***ime.unicamp.br)

Abstract: 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. It is natural to ask for conditions on the constraints under which AKKT implies KKT. These conditions will be called Strict Constraint Qualifications (SCQ). In this paper we define a Cone-Continuity Property (CCP) that will be showed to be the weakest possible SCQ. Its relation with other constraint qualifications will also be clarified. In particular, it will be proved that CCP is strictly weaker than the Constant Positive Generator (CPG) constraint qualification.

Keywords: Constrained optimization, Optimality conditions, Constraint qualifications, KKT conditions, Approximate KKT conditions

Category 1: Nonlinear Optimization (Constrained Nonlinear Optimization )

Citation:

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Entry Submitted: 02/13/2015
Entry Accepted: 02/13/2015
Entry Last Modified: 02/13/2015

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