## Clarke’s tangent cones and the boundaries of closed sets in $$\mathbb{R}^n$$.(English)Zbl 0443.26010

### MSC:

 26B05 Continuity and differentiation questions 26B25 Convexity of real functions of several variables, generalizations 49K99 Optimality conditions

Zbl 0307.26012
Full Text:

### References:

 [1] Clarke, F.H., Necessary conditions for nonsmooth problems in optimal control and the calculus of variations, () · Zbl 0612.49002 [2] Clarke, F.H., Generalized gradients and applications, Trans. am. math. soc., 205, 247-262, (1975) · Zbl 0307.26012 [3] {\scClarke} F.H. & {\scAubin} J.P., Monotone invariant solutions to differential inclusions, to appear. · Zbl 0405.34049 [4] Hiriart-Urruty, J.B., Contributions á la programmation mathématique: cas déterministe et stochastique, () · Zbl 0324.93042 [5] Hiriart-Urruty, J.-B., Tangent cones, generalized gradients and mathematical programming in Banach spaces, Math. op. research, (1978) · Zbl 0409.90086 [6] Hestenes, M., Optimization theory: the finite-dimensional case, (1975), Wiley New York · Zbl 0327.90015 [7] Rockafellar, R.T., Convex analysis, (1970), Princeton Univ. Press · Zbl 0229.90020 [8] Clarke, F.H., The Euler-Lagrange differential inclusion, J. diff. eqns, 19, 80-90, (1975) · Zbl 0323.49021 [9] Clarke, F.H., Necessary conditions for a general control problem, (), 257-278 [10] Clarke, F.H., The maximum principle under minimal hypotheses, S.I.A.M. J. control opt., 14, 1078-1091, (1976) · Zbl 0344.49009 [11] Clarke, F.H., The generalized problem of Bolza, S.I.A.M. J. control opt., 14, 682-699, (1976) · Zbl 0333.49023 [12] Clarke, F.H., Extremal arcs and extended Hamiltonian systems, Trans. am. math. soc., 231, 349-367, (1977) · Zbl 0369.49011 [13] Clarke, F.H., A new approach to Lagrange multipliers, Math. op. research, 1, 165-174, (1976) · Zbl 0404.90100 [14] Rockafellar, R.T., Conjugate convex functions in optimal control and the calculus of variations, J. math. analysis applic., 32, 174-222, (1970) · Zbl 0218.49004 [15] Rockafellar, R.T., State constraints in convex problems of Bolza, S.I.A.M. J. control, 10, 691-715, (1972) · Zbl 0224.49003 [16] Rockafellar, R.T., Dual problems of Lagrange for arcs of bounded variation, (), 155-192 · Zbl 0121.14803 [17] {\scRockafellar} R.T., Generalized directional derivatives and subgradients of nonconvex functions, Can. J. Math., to appear. · Zbl 0447.49009 [18] Rockafellar, R.T., Level sets and continuity of conjugate convex functions, Trans. am. math. soc., 123, 46-63, (1966) · Zbl 0145.15802 [19] {\scRockafellar} R.T., Directionally Lipschitzian functions and subdifferential calculus, Proc. Lond. math. Soc., to appear. · Zbl 0413.49015 [20] Caffarelli, L.A., The regularity of free boundaries in higher dimensions, Acta math., stockh., 139, 3-4, 155-184, (1977) · Zbl 0386.35046 [21] Friedman, A.; Kinderlehrer, D., A one phase stephan problem, Ind. univ. math. J., 24, 1005-1036, (1975)
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