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Clarke regular graph; necessary conditions; tangent cone; locally Lipschitz objective function; set-valued map; Clarke normal cone; generalized gradient; contingent cone

References:

[1] J.-P. Aubin I. Ekeland: **Applied Nonlinear Analysis**. Wiley, New York 1984. MR 0749753

[2] J. M. Borwein: **Multivalued convexity: a unified approach to equality and inequality constraints**. Math. Programming 13 (1977), 163-180.

[3] F. H. Clarke: **Optimization and Nonsmooth Analysis**. Wiley, New York 1983. MR 0709590 | Zbl 0582.49001

[4] P. H. Dien P. H. Sach: **Further properties of the regularity of inclusion systems**. Preprint 87-21, Inst. of Mathematics, Hanoi 1987.

[5] J.-В. Hiriart-Urruty: **Gradients generalisés de fonctions marginales**. SIAM J. Control Optim. 16(1978), 301-316. DOI 10.1137/0316019 | MR 0493610 | Zbl 0385.90099

[6] A. D. Ioffe: **Necessary and sufficient conditions for a local minimum. Part 1: A reduction theorem and first order conditions**. SIAM J. Control Optim. 17 (1979), 245-250. DOI 10.1137/0317019 | MR 0525025

[7] B. N. Pschenichnyi: **Convex set-valued mappings and their adjoints**. Kibernetika 3 (1972), 94-102 (in Russian).

[8] B. N. Pschenichnyi: **Convex Analysis and Extremal Problems**. Nauka, Moscow 1982 (in Russian).

[9] S. M. Robinson: **Generalized equations and their solutions. Part II: Applications to nonlinear programming**. Univ. Wisconsin-Madison, Technical Summary Rep. # 2048, 1980.

[10] R. T. Rockafellar: **Directional differentiability of the optimal value function in a nonlinear programming problem**. Math. Prog. Study 21 (1984), 213-226. MR 0751251 | Zbl 0546.90088

[11] P. H. Sach: **Regularity, calmness and support principle**. Optimization 19 (1988), 13 - 27. DOI 10.1080/02331938808843311 | MR 0926215 | Zbl 0648.49016