Abstract
We consider Clarke's subdifferentials of minimum functions with constrained variables. Upper bounds are obtained on the subdifferentials of the minimum functions. These bounds are shown to be more accurate than previously published bounds.
Similar content being viewed by others
Literature Cited
B. N. Pshenichnyi, Convex Analysis and Extremal Problems [in Russian], Nauka, Moscow (1980).
R. T. Rockafellar, Convex Analysis, Princeton Univ. Press (1970).
V. L. Makarov and A. M. Rubinov, Mathematical Theory of Economic Dynamics and Equilibrium [in Russian], Nauka, Moscow (1973).
J.-B. Hiriart-Urruty, “Gradients généralisés de fonctions marginales,” SIAM J. Contr. Optim.,16, 301–316 (1978).
J. Gauvin and F. Dubeau, “Differential properties of the marginal functions in mathematical programming,” Math. Progr. Study,19, 101–119 (1982).
R. T. Rockafellar, “Lagrange multipliers and subderivatives of optimal value functions in nonlinear programming,” Math. Progr. Study,17, 28–66 (1982).
B. Gollan, “On the marginal fuction in nonlinear programming,” Math. Oper. Res.,9, 208–221 (1984).
L. I. Minchenko, “Computing subdifferentials of marginal functions,” Kibernetika, No. 2, 71–76 (1986).
B. N. Pshenichnyi, Necessary Conditions of Extremum [in Russian], Nauka, Moscow (1982).
F. Clarke, “Generalized gradients and applications,” Trans. AMS,205, 247–262 (1975).
F. Clarke, “A new approach to Lagrange mulitpliers,” Math. Oper. Res.,2, 165–174 (1976).
R. T. Rockafellar,“Generalized subgradients in mathematical programming,” in: Mathematical Programming, The State of Art, Bonn (1982), pp. 368–390.
W. Hogan, “Point-to-set maps in mathematical programming,” SIAM Rev.,15, 591–603 (1973).
R. T. Rockafellar, “Generalized directional derivatives and subgradients of nonconvex functions,” Can. J. Math.,32, 257–280 (1980).
J.-B. Hiriart-Urruty, “Conditions necessaires d'optimalité en programmation non differentiable,” C.R. Acad. Sci. Paris,283, A843-A846 (1976).
L. Mintchenko and N. Rahali, “Sur les gradients generalisés de fonctions marginales,” Cahiers Math. Alger., No. 2, 11–23 (1987).
Additional information
Translated from Kibernetika, No. 5, pp. 83–85, September–October, 1989.
Rights and permissions
About this article
Cite this article
Minchenko, L.I. Computation of subdifferentials of marginal functions using the distance function. Cybern Syst Anal 25, 667–671 (1989). https://doi.org/10.1007/BF01075226
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01075226