On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. (English) Zbl 1321.49031
Summary: This paper mainly deals with the study of directional versions of metric regularity and metric subregularity for general set-valued mappings between infinite-dimensional spaces. Using advanced techniques of variational analysis and generalized differentiation, we derive necessary and sufficient conditions, which extend even the known results for the conventional metric regularity. Finally, these results are applied to non-smooth optimization problems. We show that at a locally optimal solution, M-stationarity conditions are fulfilled if the constraint mapping is subregular with respect to one critical direction, and that for every critical direction an M-stationarity condition, possibly with different multipliers, is fulfilled.
MSC:
| 49J53 | Set-valued and variational analysis |
| 49J52 | Nonsmooth analysis |
| 49K27 | Optimality conditions for problems in abstract spaces |
| 90C48 | Programming in abstract spaces |
Keywords:
set-valued mappings; metric regularity; subregularity; non-smooth optimization problems; M-stationarityReferences:
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