Primal–Dual Stability in Local Optimality
Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem’s parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multiplier vector associated with it exhibit that depende...
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| Veröffentlicht in: | Journal of optimization theory and applications Jg. 203; H. 2; S. 1325 - 1354 |
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| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
New York
Springer US
01.11.2024
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| Schlagworte: | |
| ISSN: | 0022-3239, 1573-2878 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem’s parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multiplier vector associated with it exhibit that dependence as a primal–dual pair. In classical nonlinear programming, such advantageous behavior is tied to the combination of the standard strong second-order sufficient condition (SSOC) for local optimality and the linear independent gradient condition (LIGC) on the active constraint gradients. But although second-order sufficient conditons have successfully been extended far beyond nonlinear programming, insights into what should replace constraint gradient independence as the extended dual counterpart have been lacking. The exact answer is provided here for a wide range of optimization problems in finite dimensions. Behind it are advances in how coderivatives and strict graphical derivatives can be deployed. New results about strong metric regularity in solving variational inequalities and generalized equations are obtained from that as well. |
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| ISSN: | 0022-3239 1573-2878 |
| DOI: | 10.1007/s10957-024-02467-6 |