On proto-differentiability of generalized perturbation maps |
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Authors: | GM Lee NQ Huy |
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Institution: | a Department of Applied Mathematics, Pukyong National University, Pusan, Republic of Korea b Department of Mathematics, Hanoi Pedagogical University No. 2, Xuan Hoa, Phuc Yen, Vinh Phuc, Viet Nam |
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Abstract: | This paper is devoted to the sensitivity analysis in optimization problems and variational inequalities. The concept of proto-differentiability of set-valued maps (see R.T. Rockafellar, Proto-differentiability of set-valued mappings and its applications in optimization, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989) 449-482]) plays the key role in our investigation. It is proved that, under some suitable qualification conditions, the generalized perturbation maps (that is, the solution set map to a parameterized constraint system, to a parameterized variational inequality, or to a parameterized optimization problem) are proto-differentiable. |
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Keywords: | Optimization Variational inequality Multifunction Perturbation map Proto-differentiability |
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