## Taiwanese Journal of Mathematics

### OPTIMALITY CONDITIONS FOR PORTFOLIO OPTIMIZATION PROBLEMS WITH CONVEX DEVIATION MEASURES AS OBJECTIVE FUNCTIONS

#### Abstract

In this paper we derive by means of the duality theory necessary and sufficient optimality conditions for convex optimization problems having as objective function the composition of a convex function with a linear mapping defined on a finite-dimensional space with values in a Hausdorff locally convex space. We use the general results for deriving optimality conditions for two portfolio optimization problems having as objective functions different convex deviation measures.

#### Article information

Source
Taiwanese J. Math., Volume 13, Number 2A (2009), 515-533.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500405353

Digital Object Identifier
doi:10.11650/twjm/1500405353

Mathematical Reviews number (MathSciNet)
MR2500004

Zentralblatt MATH identifier
1183.46068

#### Citation

Ioan Boţ, Radu; Lorenz, Nicole; Wanka, Gert. OPTIMALITY CONDITIONS FOR PORTFOLIO OPTIMIZATION PROBLEMS WITH CONVEX DEVIATION MEASURES AS OBJECTIVE FUNCTIONS. Taiwanese J. Math. 13 (2009), no. 2A, 515--533. doi:10.11650/twjm/1500405353. https://projecteuclid.org/euclid.twjm/1500405353

#### References

• C. M. Chen T. H. Chang, Some results for the family KKM(X,Y) and the $\Phi$-mapping, J. Math. Anal. Appl., 329 (2007), 92-101.
• S. S. Chang, B. S. Lee, X. Wu, Y. J. Cho, G. M. Lee, On the generalized quasivariational inequality problems, J. Math. Anal. Appl., 203 (1996), 686-711.
• T. H. Chang, Y. Y. Huang, J. C. Jeng, K. W. Kuo, On S-KKM property and related topics, J. Math. Anal. Appl., 229 (1999), 212-227.
• T. H. Chang, C. L. Yen, KKM property and fixed point theorems, J. Math. Anal. Appl., 203 (1996), 224-235.
• X. P. Ding, Coincidence theorems in topologicalspaces and their applications, Applied. Math. Lett., 12 (1999), 99-105.
• P. M. Fitzpatrick, W. V. Petryshyn, Fixed point theorems for multivalued noncompact inward mappings, J. Math. Anal. Appl., 46 (1974), 756-767.
• Ky Fan, A generalization of Tychonoff's fixed point theorem, Math. Ann., 142 (1961), 305-310.
• H. C. Hsu, Fixed point theorems on almost convex sets, Thesis, Dep. of Math, Cheng Kung University, \bf (2003).
• J. C. Jeng, H. C. Hsu, Y. Y. Huang, Fixed point theorems for multifunctions having KKM property on almost convex sets. J. Math. Ann. Appl., 319 (2006), 187-198.
• V. Klee, Leray-Schauder theory without locally convexity, Math. Ann., 141 (1960), 286-297.
• B. Knaster, C. Kurnatoaski, S. Mazurkiewicz, Ein Beweis des Fixpunksatzes fur n-dimensionale simplexe, Fund. Math., 14 (1929), 132-137.
• L. J. Lin, Applications of a fixed point theorems in $G$-convex spaces, Nonlinear Anal., 46 (2001), 601-608.
• L. J. Lin, System of coincidence theorems with applications, J. Math. Anal. Appl., 285 (2003), 408-418.
• G. J. Minty, On the maximal domain of a monotone function, Michigan Math. J., 8 (1961), 179-182.
• G. Q. Tian, Generalizations of $KKM$ theorem and Ky Fan minimax inequality with applications to maximal elements, price equalibrium and complementarity, J. Math. Anal. Appl., 170 (1992), 457-471.