Lipschitzian Stability in Optimization: The Role of Nonsmooth Analysis
The motivations of nonsmooth analysis are discussed. Applications are given to the sensitivity of optimal values, the interpretation of Lagrange multipliers, and the stability of constraint systems under perturbation.
KeywordsMold Hull Aire
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- F.H. Clarke, Optimization and Nonsmooth Analysis,Wiley-Interscience, New York, 1983.Google Scholar
- R.T. Rockafellar, Convex Analysis, Princeton University Press, Princeton NJ, 1970.Google Scholar
- R.T. Rockafellar, Favorable classes of Lipschitz continuous functions in subgradient optimization, Processes in Nondi,fferentiable Optimization, E. Nurminski (ed.), IIASA Collaborative Proceeding Series, International Institute for Applied Systems Analysis, Laxenburg, Austria, 1982, pp. 125 - 143.Google Scholar
- S. Saks, Theory of the Integral, Monografie Matematyczne Ser., no. 7, 1937; 2nd rev.ed. Dover Press, New York, 1964.Google Scholar
- R.T. Rockafellar, Extensions of subgradient calculus with applications to optimization, J. Nonlinear Anal., to appear in 1985.Google Scholar
- R.W. Chaney, Math. Oper. Res. 9 (1984).Google Scholar
- R.T. Rockafellar, Generalized directional derivatives and subgradients of non-convex functions, Canadian J. Math. 32 (1980), pp. 157 - 180.Google Scholar
- R.T. Rockafellar, The Theory of Subgradients and its Applications to Problems of Optimization: Convex and Nonconvex Functions, Heldermann Verlag, West Berlin, 1981.Google Scholar
- R.T. Rockafellar, Lipschitzian properties of multifunctions, J. Nonlin. Anal., to appear in 1985.Google Scholar
- R.T. Rockafellar, Convex algebra and duality in dynamic models of production, in Mathematical Models of Economic (J. Los, ed.), North-Holland, 1973, pp.351–378.Google Scholar
- R.T. Rockafellar, Monotone Processes of Convex and Concave Type, Memoir no. 77, Amer. Math. Soc., Providence RI, 1967.Google Scholar
- R.T. Rockafellar, Maximal monotone relations and the second derivatives of nonsmooth functions, Ann. Inst. H. Poincaré, Analyse Non Linéaire 2 (1985), pp. 167 - 184.Google Scholar