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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

On a Conjecture in Second-Order Optimality Conditions

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Author(s):
Behling, Roger [1] ; Haeser, Gabriel [2] ; Ramos, Alberto [3] ; Viana, Daiana S. [4]
Total Authors: 4
Affiliation:
[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
Total Affiliations: 4
Document type: Journal article
Source: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 176, n. 3, p. 625-633, MAR 2018.
Web of Science Citations: 3
Abstract

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)

FAPESP's process: 13/05475-7 - Computational methods in optimization
Grantee:Sandra Augusta Santos
Support type: Research Projects - Thematic Grants
FAPESP's process: 16/02092-8 - On the second-order information in nonlinear optimization
Grantee:Gabriel Haeser
Support type: Scholarships abroad - Research