ε-Optimality for Nonsmooth Programming on a Hilbert Space
Conference paper
Abstract
Lagrange multiplier rules characterizing ε-optimality/ε-efficiency for nonsmooth programming problems on a real Hilbert space are established in terms of the limiting subgradients.
Keywords
Nonlinear programming limiting subgradient variational principle approximate solution Lagrange multiplier rulePreview
Unable to display preview. Download preview PDF.
References
- Borwein, J. M. and Preiss, D. (1987), A smooth variational principle with applications to subdifferentiability and to differentiability of convex functions, Trans. Amer. Math. Soc., Vol. 303, pp. 517–527.MathSciNetCrossRefGoogle Scholar
- Clarke, F. H. (1983), Optimization and Nonsmooth Analysis, Wiley, New York.Google Scholar
- Clarke, F. H., Ledyavev, Y. S., Stern, R. J. and Wolenski, P. R. (1998), Nonsmooth Analysis and Control Theory, Springer, Berlin.Google Scholar
- Ekeland, I. (1974), On the variational principle, J. Math. Anal. Appl., Vol. 47, pp. 324–353.MATHMathSciNetCrossRefGoogle Scholar
- Hamel, A. (2001), An multiplier ε-Lagrange rule for a mathematical programming on Banach spaces, Optimization, Vol. 49, pp. 137–149.MATHMathSciNetGoogle Scholar
- Kruger, A.Y. and Mordukhovich, B.S. (1980), Extremal points and the Euler equation in nonsmooth optimization, Dokl. Akad. Nauk BSSR, Vol. 24, pp. 684–687.MathSciNetGoogle Scholar
- Liu, J. C. (1991), ε-duality theorem of nondifferentiable nonconvex multiobjective programming, J. Optim. Th. Appl., Vol. 69, pp. 153–167.MATHCrossRefGoogle Scholar
- Liu, J. C. (1996), ε-Pareto optimality for nondifferentiable multiobjective programming via penalty function, J. Math. Anal. Appl., Vol. 198, pp. 248–261.MATHMathSciNetCrossRefGoogle Scholar
- Loridan, P. (1982), Necessary conditions for ε-optimality, Math. Prog. Study, Vol. 19, pp. 140–152.MathSciNetGoogle Scholar
- Mordukhovich, B.S. (1976), Maximum principle in the problem of time optimal control with nonsmooth constraints, J. Appl. Math. Mech., Vol. 40, pp. 960–969.MATHMathSciNetCrossRefGoogle Scholar
- Mordukhovich, B.S. (1984), Nonsmooth analysis with nonconvex generalized differentials and adjoint mappings, Dokl. Akad. Nauk BSSR, Vol. 28, pp. 976–979.MATHMathSciNetGoogle Scholar
- Mordukhovich, B.S. and Shao, Y. (1996), Nonsmooth sequential analysis in Asplund spaces, Trans. Amer. Math. Soc., Vol. 348, pp. 1235–1280.MathSciNetCrossRefGoogle Scholar
- Mordukhovich, B.S. and Wang, B. (2003), Necessary suboptimality and optimality conditions via variational principles, SIAM J. Control Optim., Vol. 41, pp. 623–640.MathSciNetCrossRefGoogle Scholar
Copyright information
© Springer Science + Business Media, Inc. 2005