| Full text | |
| Author(s): |
Andreani, Roberto
[1]
;
Gomez, Walter
[2]
;
Haeser, Gabriel
[3]
;
Mito, Leonardo M.
[3]
;
Ramos, Alberto
[4]
Total Authors: 5
|
| Affiliation: | [1] Univ Estadual Campinas, Dept Appl Math, BR-13083970 Campinas - Brazil
[2] Univ La Frontera, Dept Math Engn, Temuco 4811230 - Chile
[3] Univ Sao Paulo, Dept Appl Math, BR-05508090 Sao Paulo - Brazil
[4] Univ Fed Parana, Dept Math, BR-81530015 Curitiba, Parana - Brazil
Total Affiliations: 4
|
| Document type: | Journal article |
| Source: | MATHEMATICS OF OPERATIONS RESEARCH; p. 1-26, DEC 2021. |
| Web of Science Citations: | 1 |
| Abstract | |
Sequential optimality conditions play a major role in proving stronger global convergence results of numerical algorithms for nonlinear programming. Several extensions are described in conic contexts, in which many open questions have arisen. In this paper, we present new sequential optimality conditions in the context of a general nonlinear conic framework, which explains and improves several known results for specific cases, such as semidefinite programming, second-order cone programming, and nonlinear programming. In particular, we show that feasible limit points of sequences generated by the augmented Lagrangian method satisfy the so-called approximate gradient projection optimality condition and, under an additional smoothness assumption, the so-called complementary approximate Karush-Kuhn-Tucker condition. The first result was unknown even for nonlinear programming, and the second one was unknown, for instance, for semidefinite programming. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |
| FAPESP's process: | 17/18308-2 - Second-order optimality conditions and algorithms |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 18/24293-0 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 17/17840-2 - Error estimation in nonlinear optimization |
| Grantee: | Leonardo Makoto Mito |
| Support Opportunities: | Scholarships in Brazil - Doctorate |
| FAPESP's process: | 13/05475-7 - Computational methods in optimization |
| Grantee: | Sandra Augusta Santos |
| Support Opportunities: | Research Projects - Thematic Grants |