A generic result in vector optimization
© Alexander J. Zaslavski. 2006
Received: 17 November 2005
Accepted: 24 March 2006
Published: 1 June 2006
We study a class of vector minimization problems on a complete metric space such that all its bounded closed subsets are compact. We show that for most (in the sense of Baire category) problems in the class the sets of minimal values are infinite.
- Chen G-Y, Huang X, Yang X: Vector Optimization, Lecture Notes in Economics and Mathematical Systems. Volume 541. Springer, Berlin; 2005:x+306.Google Scholar
- Dauer JP, Gallagher RJ: Positive proper efficient points and related cone results in vector optimization theory. SIAM Journal on Control and Optimization 1990,28(1):158–172. 10.1137/0328008MATHMathSciNetView ArticleGoogle Scholar
- Ehrgott M, Gandibleux X (Eds): Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys, International Series in Operations Research & Management Science. Volume 52. Kluwer Academic, Massachusetts; 2002:xxii+496.Google Scholar
- Jahn J: Vector Optimization. Theory, Applications, and Extensions. Springer, Berlin; 2004:xiv+465.MATHGoogle Scholar
- Tanino T: Stability and sensitivity analysis in convex vector optimization. SIAM Journal on Control and Optimization 1988,26(3):521–536. 10.1137/0326031MATHMathSciNetView ArticleGoogle Scholar
- Wei Z, Qi L, Birge JR: A new method for nonsmooth convex optimization. Journal of Inequalities and Applications 1998,2(2):157–179. 10.1155/S1025583498000101MATHMathSciNetGoogle Scholar
- Zaslavski AJ: Generic existence of solutions of nonconvex optimal control problems. Abstract and Applied Analysis 2005,2005(4):375–421. 10.1155/AAA.2005.375MATHMathSciNetView ArticleGoogle Scholar
- Zaslavski AJ: Turnpike Properties in the Calculus of Variations and Optimal Control, Nonconvex Optimization and Its Applications. Volume 80. Springer, New York; 2006:xxii+395.MATHGoogle Scholar
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