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On Constraint Qualifications for Second-Order Optimality Conditions Depending on a Single Lagrange Multiplier.

Alberto Ramos (albertoramos***at***ufpr.br)
Gabriel Haeser (ghaeser***at***ime.usp.br)

Abstract: Second-order optimality conditions play an important role in continuous optimization. In this paper, we present and discuss new constraint qualifications to ensure the validity of some well-known second-order optimality conditions. Our main interest is on second-order conditions that can be associated with numerical methods for solving constrained optimization problems. Such conditions depend on a single Lagrange multiplier, instead of the whole set of Lagrange multipliers, and they are consistent with second-order algorithms where, usually, at each iteration, one only has access to a single approximate Lagrange multiplier. For each condition, we characterize the weakest second-order constraint qualification that guarantees its fulfillment at local minimizers, while proposing new weak conditions implying them. Relations with other constraint qualifications stated in the literature are discussed.

Keywords: Nonlinear optimization, constraint qualifications, second-order optimality conditions

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )


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Entry Submitted: 11/28/2019
Entry Accepted: 11/29/2019
Entry Last Modified: 11/29/2019

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