[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.14403/jcms.2016.29.1.29

ON SOLUTION SET FOR CONVEX OPTIMIZATION PROBLEM WITH CONVEX INTEGRABLE OBJECTIVE FUNCTION AND GEOMETRIC CONSTRAINT SET

Lee, Gue Myung (Department of Applied Mathematics, Pukyong National University)
Lee, Jae Hyoung (Department of Applied Mathematics, Pukyong National University)

Publication Information

Journal of the Chungcheong Mathematical Society / v.29, no.1, 2016 , pp. 29-35 More about this Journal

Abstract

In this paper, we consider a convex optimization problem with a convex integrable objective function and a geometric constraint set. We characterize the solution set of the problem when we know its one solution.

Keywords

solution set; subdifferential; convex optimization problem; convex integrable objective function; geometric constraint set;

Citations & Related Records

Reference

1	J. -P. Aubin and H. Frankowska, Set-Valued Analysis, Birkhauser Boston, 1990.
2	J. V. Burke and M. Ferris, Characterization of solution sets of convex programs, Oper. Res. Lett. 10 (1991), 57-60. DOI
3	M. Castellani and M. Giuli, A characterization of the solution set of pseudoconvex extremum problems, J. Convex Anal. 19 (2012), 113-123.
4	F. H. Clarke, Yu. S. Ledyaev, R. J. Stern and P. R. Wolenski, Nonsmooth Analysis and Control Theory, Springer-Verlag, New York, Inc., 1998.
5	V. Jeyakumar, G. M. Lee, and N. Dinh, Lagrange multiplier conditions characterizing optimal solution sets of cone-constrained convex programs, J. Optim. Theor. Appl. 123 (2004), 83-103. DOI
6	V. Jeyakumar, G. M. Lee, and N. Dinh, Characterizations of solution sets of convex vector minimization problems, Eur. J. Oper. Res. 174 (2006), 1380-1395. DOI
7	V. Jeyakumar, G, M. Lee, and G. Li, Characterizing Robust Solution Sets of Convex Programs under Data Uncertainty, J. Optim. Theory Appl. 164 (2015), 407-435. DOI
8	V. Jeyakumar and X. Q. Yang, On characterizing the solution sets of pseudolinear programs, J. Optim. Theory Appl. 87 (1995), 747-755. DOI
9	C. S. Lalitha and M. Mehta, Characterizations of solution sets of mathematical programs in terms of Lagrange multipliers, Optimization 58 (2009), 995-1007. DOI
10	O. L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett. 7 (1988), 21-26. DOI
11	J. P. Penot, Characterization of solution sets of quasiconvex programs, J. Optim. Theory Appl. 117 (2003), 627-636. DOI
12	T. Q. Son and N. Dinh, Characterizations of optimal solution sets of convex infinite programs, TOP. 16 (2008), 147-163. DOI
13	Z. L. Wu and S. Y. Wu, Characterizations of the solution sets of convex programs and variational inequality problems, J. Optim. Theory Appl. 130 (2006), 339-358.
14	C. Zalinescu, Convex Analysis in General Vector Spaces, World Scientific, 2002.
15	K. Q. Zhao and X. M. Yang, Characterizations of the solution set for a class of nonsmooth optimization problems, Optim. Lett. 7 (2013), 685-694. DOI