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(Referência obtida automaticamente do Web of Science, por meio da informação sobre o financiamento pela FAPESP e o número do processo correspondente, incluída na publicação pelos autores.)

A second-order optimality condition with first- and second-order complementarity associated with global convergence of algorithms

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Autor(es):
Haeser, Gabriel
Número total de Autores: 1
Tipo de documento: Artigo Científico
Fonte: COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 70, n. 2, p. 615-639, JUN 2018.
Citações Web of Science: 2
Resumo

We develop a new notion of second-order complementarity with respect to the tangent subspace related to second-order necessary optimality conditions by the introduction of so-called tangent multipliers. We prove that around a local minimizer, a second-order stationarity residual can be driven to zero while controlling the growth of Lagrange multipliers and tangent multipliers, which gives a new second-order optimality condition without constraint qualifications stronger than previous ones associated with global convergence of algorithms. We prove that second-order variants of augmented Lagrangian (under an additional smoothness assumption based on the Lojasiewicz inequality) and interior point methods generate sequences satisfying our optimality condition. We present also a companion minimal constraint qualification, weaker than the ones known for second-order methods, that ensures usual global convergence results to a classical second-order stationary point. Finally, our optimality condition naturally suggests a definition of second-order stationarity suitable for the computation of iteration complexity bounds and for the definition of stopping criteria. (AU)

Processo FAPESP: 13/05475-7 - Métodos computacionais de otimização
Beneficiário:Sandra Augusta Santos
Linha de fomento: Auxílio à Pesquisa - Temático
Processo FAPESP: 16/02092-8 - Informação de segunda-ordem em otimização não linear
Beneficiário:Gabriel Haeser
Linha de fomento: Bolsas no Exterior - Pesquisa