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Fully Hölderian stable minimum with respect to both tilt and parameter perturbations. (English) Zbl 1402.90185

Summary: When the objective function undergoes both a tilt perturbation and a general parameter perturbation, this paper considers the notions of a fully stable Hölder minimizer, a uniform Hölder growth condition, and a fully stable \((q,s)\)-minimum, where the last notion reduces to the tilt-stable minimum by A. B. Levy et al. [SIAM J. Optim. 10, No. 2, 580–604 (2000; Zbl 0965.49018)] and the fully Hölder stable minimum by B. S. Mordukhovich and T. T. A. Nghia [SIAM J. Optim. 24, No. 3, 1344–1381 (2014; Zbl 1304.49047)] as special cases by taking \((q,s)=(2,2)\) and \((q,s)=(2,1)\), respectively. Under weak-\((\mathcal{BCQ})\) (a new constraint qualification), by using the techniques of variational analysis, we establish relationships among these notions and provide several characterizations for fully stable \((q,s)\)-minima, which improve and generalize some existing results in the recent literature.

MSC:

90C31 Sensitivity, stability, parametric optimization
90C30 Nonlinear programming
49J52 Nonsmooth analysis
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