Quasi-contingent derivatives and studies of higher-orders in nonsmooth optimization. (English) Zbl 1492.90192
Summary: We consider higher-order conditions and sensitivity analysis for solutions to equilibrium problems. The conditions for solutions are in terms of quasi-contingent derivatives and involve higher-order complementarity slackness for both the objective and the constraints and under Hölder metric subregularity assumptions. For sensitivity analysis, a formula of this type of derivative of the solution map to a parametric equilibrium problem is established in terms of the same types of derivatives of the data of the problem. Here, the concepts of a quasi-contingent derivative and critical directions are new. We consider open-cone solutions and proper solutions. We also study an important and typical special case: weak solutions of a vector minimization problem with mixed constraints. The results are significantly new and improve recent corresponding results in many aspects.
MSC:
| 90C46 | Optimality conditions and duality in mathematical programming |
| 90C31 | Sensitivity, stability, parametric optimization |
| 90C30 | Nonlinear programming |
| 49J52 | Nonsmooth analysis |
| 49J53 | Set-valued and variational analysis |
Keywords:
Karush-Kuhn-Tucker conditions; higher-order complementarity slackness; Hölder metric subregularity; quasi-contingent derivative; critical directions; derivative of solution mapReferences:
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