| Full text | |
| Author(s): |
Total Authors: 4
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| 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
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| 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 |