Abstract
In the paper an optimization problem on locally convex spaces is studied. This problem is a generalization of both the classical optimization and those which involve set functions. First and second order optimality conditions and, for closely convex case, a duality theorem are stated.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aleman, A., On some generalization of convex sets and convex functions. Anal. Numer. Theor. Approx (Cluj) 14 (1985), 1–6.
Begis, D. and Glowinski, R., Application de la méthode des éléments finis à l’approximation d’un problème de domaine optimal. Méthodes de résolution des problèmes approchés. Applied Math. and Opt. 2 (1975), 130–169.
Cea, J., Gioan, A. and Michel, J., Quelque rèsultats sur l’identification des domaines. Calcolo 10 (1973), 207–233.
Cobzas, S. T. and Muntean, I., Duality relations and characterizations of best approximation for p-convex sets. Mathematica- Revue d’analyse num. et de théorie de l’approx. Tome 16, 2 (1987), 95–108.
Chou, J. H., Hsia, W. S. and Lee, T. Y., Second order optimality conditions for mathematical programming set functions. J. Austral. Math. Soc. (ser. B) 26 (1985), 383–394.
Deâk, E., ‘ber konvexe und interne Funktionen sowie eine gemeinsame verallgemeinerung von beiden. Ann. Univ. Eötvös Sci. Budapest. Sect Math. 5 (1962), 109–154.
Flett, T. M., Differential Analysis, Cambridge University Press, 1980.
Frölicher, A. and Kriegl, A., Linear spaces and differentiation theory. John Wiley and Sons, 1988.
Hoffmann, K.-H. and Kornstaedt, H.-J., Higher order necessary conditions in abstract mathematical programming. J. Optim. Theory Appl. 26 (1978), 533–568.
Illés, T., Joó, I. and Kassay, G., On a nonconvex Farkas theorem and its application in optimization theory, Eötvös Lorand Tudoma’nyegyetem Operâciókutatâsi Tanszék, Report 1992–03, 3–11.
Karlin, S., Mathematical Methods and Theory in Games, Programming and Economics. Vol 1, Reading Mass: Addision Wesley, 1959.
Kolumbân, J. and Blaga, L., On the weakly convex sets, STUDIA Univ. Babes-Bolyai, Mathematica, 35 (1990), 13–20.
Koshi, S., Lai, H. C. and Komuro, N., Convex programming on spaces of measurable functions, Hokkaydo Math J. 14 (1985), 75–84.
Lai, H. C., Yang, S. S. and Hwang G., Duality in mathematical programming of set functions: On Fenchel duality theorem. J. Math. Appl 95 (1983), 223–234.
Lai, H. C. and Yang, S. S., Saddle point and duality in the optimization theory of the convex set functions. J. Austral Math. Soc. (ser B) 24 (1982), 130–137.
Lai H. C. and Lin, L. J., The Fenchel-Moreau theorem for set functions, Proceedings of the American Mathematical Society, 103 (1988), 85–91.
McCormick, G. P., Second order conditions for constrained minima, SIAM J. Appl Math. 15 (1967), 641–652.
Morris, R. J. T., Optimal constrained selection of measurable subsets, J. Math. Anal. Appl. 70 (1979), 546–562.
Muntean, I., A multiplier rule in p-convex programming, “Babes- Bolyai” University, Faculty of Math., Research seminar’s. Seminar on Math. Analysis, Preprint No. 7 (1985), 149–156.
Neumann, J. von, On complete topological spaces, Trans. Amer. Math. Soc., 37 (1935), 1–20.
Sokolowski, J. and Zolesio, J. P., Introduction to Shape Optimization, Shape Sensitivity Analysis, Springer-Verlag, Berlin—Heidelberg, 1992.
Wang, P. K. C., On a class of optimization problems involving domain variations, “International Symposium on New Trends in System Analysis, Versailles, France, Dec. 1976”, Lecture Notes in Control and Information Sciences, No. 2, Springer-Verlag, 1977.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Blaga, L., Kolumbán, J. (1994). Optimization on closely convex sets. In: Komlósi, S., Rapcsák, T., Schaible, S. (eds) Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-46802-5_2
Download citation
DOI: https://doi.org/10.1007/978-3-642-46802-5_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-57624-2
Online ISBN: 978-3-642-46802-5
eBook Packages: Springer Book Archive