On a Conjecture in Second-Order Optimality Conditions

Autor(es)

Behling, Roger ^[1] ; Haeser, Gabriel ^[2] ; Ramos, Alberto ^[3] ; Viana, Daiana S. ^[4]

Afiliação do(s) autor(es)

^[1] Univ Fed Santa Catarina, Blumenau, SC - Brazil

^[2] Univ Sao Paulo, Dept Appl Math, Sao Paulo, SP - Brazil

^[3] Univ Fed Parana, Dept Math, Curitiba, Parana - Brazil

^[4] Univ Fed Acre, Ctr Exact & Technol Sci, Rio Branco, AC - Brazil

• Tipo de documento: Artigo Científico
• Fonte: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 176, n. 3, p. 625-633, MAR 2018.
• Citações Web of Science: 3

Resumo

In this paper, we deal with a conjecture formulated in Andreani et al. (Optimization 56:529-542, 2007), which states that whenever a local minimizer of a nonlinear optimization problem fulfills the Mangasarian-Fromovitz constraint qualification and the rank of the set of gradients of active constraints increases at most by one in a neighborhood of the minimizer, a second-order optimality condition that depends on one single Lagrange multiplier is satisfied. This conjecture generalizes previous results under a constant rank assumption or under a rank deficiency of at most one. We prove the conjecture under the additional assumption that the Jacobian matrix has a smooth singular value decomposition. Our proof also extends to the case of the strong second-order condition, defined in terms of the critical cone instead of the critical subspace. (AU)

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