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

Autor(es)

Haeser, Gabriel

• 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