| Full text | |
| Author(s): |
Haeser, Gabriel
Total Authors: 1
|
| Document type: | Journal article |
| Source: | COMPUTATIONAL OPTIMIZATION AND APPLICATIONS; v. 70, n. 2, p. 615-639, JUN 2018. |
| Web of Science Citations: | 2 |
| Abstract | |
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) | |
| 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 |