Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T10:20:28.348Z Has data issue: false hasContentIssue false
  • English
  • Français

Second order optimality conditions for mathematical prograramming with set functions

Published online by Cambridge University Press:  17 February 2009

J. H. Chou ,
Wei-Shen Hsia  and
Tan-Yu Lee
Tan-Yu Lee
Affiliation:
Department of Mathematics, The University of Alabama, University, Alabama 35486, U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Second order necessary and sufficient conditions are given for a class of optimization problems involving optimal selection of a measurable subset from a given measure subspace subject to set function inequalities. Relations between twice-differentiability at Ω and local convexity at Ω are also discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 26 , Issue 3 , January 1985 , pp. 284 - 292
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Begis, D. and Glowinski, R., “Application de la méthode des éléments finis àl'approximation d'un problème de domaine optimal. Méthodes de résolution des problées approchés”, App. Math. Optim. 2 (1975), 130–169.CrossRefGoogle Scholar
[2]Ben-Tal, A. and Zowe, J., “A unified theory of first and second order conditions for extremum problems in topoological vector spaces”, in Mathematical programming study 19 (ed. Guignard, M.), (North-Holland, Amsterdam, 1981).Google Scholar
[3]Cea, J., Gioan, A. and Michel, J., “Queques résultats sur l'identification de domaines”, Calcolo 10 (1973), 133–145.CrossRefGoogle Scholar
[4]Hestenes, M. R., Optimization theory— The finite-dimensional case (Wiley, New York, 1975).Google Scholar
[5]Ioffe, A. D., “Necessary and sufficient sonditions for a local minimum. 3: Second order conditions and augmented duality”, SIAM J. Control Optim. 17 (1979), 266–288.CrossRefGoogle Scholar
[6]Lai, H. L. and Yang, S. S., “Saddle point and duality in the optimization theory of convex set functions”, J. Austral. Math. Soc. Ser. B 24 (1982), 130–137.CrossRefGoogle Scholar
[7]Lai, H. L., Yang, S. S. and Hwang, G. R., “Duality in mathematical programming of set functions: On Fenchel duality theorem”, J. Math. Anal. Appl. 95 (1983), 223–234.CrossRefGoogle Scholar
[8]Lunenberger, D. G., Optimization by vector space methods (Wiley, New York, 1969).Google Scholar
[9]Managasarian, O. L., Nonlinear programming (McGraw Hill, New York, 1969).Google Scholar
[10]Maurer, H. and Zowe, J., “First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems”, Math. Programming 16 (1979), 98–110.CrossRefGoogle Scholar
[11]Morris, Robert J. T., “Optimal constrained selection of a measurable subset”, J. Math. Anal. Appl. 70 (1979), 546–562.CrossRefGoogle Scholar
[12]Wang, P. K. C., “On a class of optimization problems involving domain variations”, in International symposium on new trends in system analysis, Versailles, France, (12 1976),Google Scholar
Lecture Notes in Control and Information Sciences 2 (Springer-Verlag, Berlin, 1977), 49.Google Scholar