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A subdifferential condition for calmness of multifunctions. (English) Zbl 0983.49010
The paper deals with the characterization of calmness property for a class of multifunctions between finite dimensional spaces. The approach relies on Mordukhovich’s nonsmooth calculus for set-valued mappings. Applications to nonlinear optimization and complementarity theory are given.

49J52Nonsmooth analysis (other weak concepts of optimality)
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)
49J53Set-valued and variational analysis
54C60Set-valued maps (general topology)
Full Text: DOI
[1] Clarke, F. H.: A new approach to Lagrange multipliers. Math. oper. Res. 1, 165-174 (1976) · Zbl 0404.90100
[2] Clarke, F. H.: Optimization and nonsmooth analysis. (1983) · Zbl 0582.49001
[3] Ioffe, A. D.: Necessary and sufficient conditions for a local minimum, part I. SIAM J. Cont. optimiz. 17, 245-265 (1979) · Zbl 0417.49027
[4] Mifflin, R.: Semismooth and semiconvex functions in constrained optimization. SIAM J. Cont. optimiz. 15, 959-972 (1977) · Zbl 0376.90081
[5] Mordukhovich, B. S.: Sensitivity analysis in nonsmooth optimization. SIAM proc. Appl. math. 58, 32-46 (1992) · Zbl 0769.90075
[6] Mordukhovich, B. S.: Complete characterization of openness, metric regularity and Lipschitzian properties of multifunctions. Trans. amer. Math. soc. 340, 1-35 (1993) · Zbl 0791.49018
[7] Mordukhovich, B. S.: Generalized differential calculus for nonsmooth and set-valued mappings. J. math. Anal. appl. 183, 250-288 (1994) · Zbl 0807.49016
[8] Outrata, J. V.: On mathematical programs with complementarity constraints. Optimiz. meth. Software 14, 117-137 (2000) · Zbl 0979.49027
[9] Rockafellar, R. T.; Wets, R. J. -B.: Variational analysis. (1997) · Zbl 0888.49001
[10] Ye, J. J.; Ye, X. Y.: Necessary optimality conditions for optimization problems with variational inequality constraints. Math. oper. Res. 22, 977-997 (1997) · Zbl 1088.90042