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A generic result in vector optimization
Journal of Inequalities and Applications volume 2006, Article number: 54027 (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.
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. 10.1137/0328008
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.
Jahn J: Vector Optimization. Theory, Applications, and Extensions. Springer, Berlin; 2004:xiv+465.
Tanino T: Stability and sensitivity analysis in convex vector optimization. SIAM Journal on Control and Optimization 1988,26(3):521–536. 10.1137/0326031
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/S1025583498000101
Zaslavski AJ: Generic existence of solutions of nonconvex optimal control problems. Abstract and Applied Analysis 2005,2005(4):375–421. 10.1155/AAA.2005.375
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.
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Zaslavski, A.J. A generic result in vector optimization. J Inequal Appl 2006, 54027 (2006). https://doi.org/10.1155/JIA/2006/54027
- Generic Result
- Minimization Problem
- Closed Subset
- Vector Optimization
- Baire Category