| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Sao Paulo, Inst Math & Stat, Sao Paulo - Brazil
[2] Univ La Plata, FCE, Dept Math, CONICET, RA-1900 La Plata, Buenos Aires - Argentina
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS; v. 149, n. 3, p. 528-539, JUN 2011. |
| Web of Science Citations: | 11 |
| Abstract | |
In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions. (AU) | |
| FAPESP's process: | 09/09414-7 - Penalty methods and optimality conditions |
| Grantee: | Gabriel Haeser |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |