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Submonotone subdifferentials of Lipschitz functions. (English) Zbl 0465.26008


MSC:

26B25 Convexity of real functions of several variables, generalizations
47H05 Monotone operators and generalizations
49J40 Variational inequalities
26B05 Continuity and differentiation questions
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References:

[1] Frank H. Clarke, Generalized gradients and applications, Trans. Amer. Math. Soc. 205 (1975), 247 – 262. · Zbl 0307.26012
[2] Frank H. Clarke, Generalized gradients of Lipschitz functionals, Adv. in Math. 40 (1981), no. 1, 52 – 67. · Zbl 0463.49017 · doi:10.1016/0001-8708(81)90032-3
[3] Gérard Lebourg, Valeur moyenne pour gradient généralisé, C. R. Acad. Sci. Paris Sér. A-B 281 (1975), no. 19, Ai, A795 – A797 (French, with English summary). · Zbl 0317.46034
[4] Robert Mifflin, Semismooth and semiconvex functions in constrained optimization, SIAM J. Control Optimization 15 (1977), no. 6, 959 – 972. · Zbl 0376.90081 · doi:10.1137/0315061
[5] George J. Minty, Monotone (nonlinear) operators in Hilbert space, Duke Math. J. 29 (1962), 341 – 346. · Zbl 0111.31202
[6] B. N. Pshenichnyi, Necessary conditions for an extremum, Translated from the Russian by Karol Makowski. Translation edited by Lucien W. Neustadt. Pure and Applied Mathematics, vol. 4, Marcel Dekker, Inc., New York, 1971. · Zbl 0764.90079
[7] R. Tyrrell Rockafellar, Convex analysis, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Reprint of the 1970 original; Princeton Paperbacks. · Zbl 0932.90001
[8] R. T. Rockafellar, The multiplier method of Hestenes and Powell applied to convex programming, J. Optimization Theory Appl. 12 (1973), 555 – 562. · Zbl 0254.90045 · doi:10.1007/BF00934777
[9] R. T. Rockafellar, Augmented Lagrangians and applications of the proximal point algorithm in convex programming, Math. Oper. Res. 1 (1976), no. 2, 97 – 116. · Zbl 0402.90076 · doi:10.1287/moor.1.2.97
[10] -, The theory of subgradients and its applications to problems of optimization, Lecture Notes, Univ. of Montreal, Feb.-March, 1978.
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