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On the Weak Second-order Optimality Condition for Nonlinear Semidefinite and Second-order Cone Programming

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Autor(es):
Fukuda, Ellen H. ; Haeser, Gabriel ; Mito, Leonardo M.
Número total de Autores: 3
Tipo de documento: Artigo Científico
Fonte: Set-Valued and Variational Analysis; v. 31, n. 2, p. 28-pg., 2023-06-01.
Resumo

Second-order necessary optimality conditions for nonlinear conic programming problems that depend on a single Lagrange multiplier are usually built under nondegeneracy and strict complementarity. In this paper we establish a condition of such type for two classes of nonlinear conic problems, namely semidefinite and second-order cone programming, assuming Robinson's constraint qualification and a weak constant rank-type property which are, together, strictly weaker than nondegeneracy. Our approach is done via a penalty-based strategy, which is aimed at providing strong global convergence results for first- and second-order algorithms. Since we are not assuming strict complementarity, the critical cone does not reduce to a subspace, thus, the second-order condition we arrive at is defined in terms of the lineality space of the critical cone. In the case of nonlinear programming, this condition reduces to the standard second-order condition widely used as second-order stationarity measure in the algorithmic practice. (AU)

Processo FAPESP: 17/18308-2 - Condições de otimalidade e algoritmos de segunda-ordem
Beneficiário:Gabriel Haeser
Modalidade de apoio: Auxílio à Pesquisa - Regular
Processo FAPESP: 18/24293-0 - Métodos computacionais de otimização
Beneficiário:Sandra Augusta Santos
Modalidade de apoio: Auxílio à Pesquisa - Temático
Processo FAPESP: 17/17840-2 - Estimativas de erro em otimização não linear
Beneficiário:Leonardo Makoto Mito
Modalidade de apoio: Bolsas no Brasil - Doutorado