Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems
-
1591
Downloads
-
2785
Views
Authors
Lu-Chuan Ceng
- Department of Mathematics, Shanghai Normal University, Shanghai 200234, China.
Abdul Latif
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.
Abstract
We study the Stampacchia equilibrium-like problems in terms of normal subdifferential for set-valued
maps and study their relations with set-valued optimization problems by the scalarization method.
Characterizations of the solution sets of generalized pseudoinvex extremum problems are established.
Share and Cite
ISRP Style
Lu-Chuan Ceng, Abdul Latif, Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 6382--6395
AMA Style
Ceng Lu-Chuan, Latif Abdul, Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems. J. Nonlinear Sci. Appl. (2016); 9(12):6382--6395
Chicago/Turabian Style
Ceng, Lu-Chuan, Latif, Abdul. "Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 6382--6395
Keywords
- Set-valued maps
- normal subdifferential
- solution set
- Stampacchia equilibrium-like problem.
MSC
References
-
[1]
M. Alshahrani, Q. H. Ansari, S. Al-Homidan, Nonsmooth variational-like inequalities and nonsmooth vector optimization, Optim. Lett., 8 (2014), 739--751
-
[2]
Q. H. Ansari, M. Rezaei, Generalized pseudolinearity, Optim. Lett., 6 (2012), 241--251
-
[3]
T. Q. Bao, B. S. Mordukhovich, Variational principles for set-valued mappings with applications to multiobjective optimization, Control Cybernet, 36 (2007), 531--562
-
[4]
L.-C. Ceng, G.-Y. Chen, X.-X. Huang, J.-C. Yao, Existence theorems for generalized vector variational inequalities with pseudomonotonicity and their applications, Taiwanese J. Math., 12 (2008), 151--172
-
[5]
L.-C. Ceng, S.-C. Huang, Existence theorems for generalized vector variational inequalities with a variable ordering relation, J. Global Optim., 46 (2010), 521--535
-
[6]
L.-C. Ceng, A. Latif, Q. H. Ansari, Y.-C. Yao, Hybrid Extragradient Method for Hierarchical Variational Inequalities, Fixed Point Theory and Appl., 2014 (2014), 35 pages
-
[7]
L.-C. Ceng, A. Latif, J.-C. Yao, On solutions of a system of variational inequalities and fixed point problems in Banach spaces, Fixed Point Theory and Appl., 2013 (2013), 34 pages
-
[8]
L.-C. Ceng, B. S. Mordukhovich, J.-C. Yao, Hybrid approximate proximal method with auxiliary variational inequality for vector optimization, J. Optim. Theory Appl., 146 (2010), 267--303
-
[9]
L.-C. Ceng, S. Schaible, J.-C. Yao, Existence of solutions for generalized vector variational-like inequalities, J. Optim. Theory Appl., 137 (2008), 121--133
-
[10]
G.-Y. Chen, X.-X. Huang, X.-Q. Yang, Vector Optimization, Set-valued and variational analysis, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin (2005)
-
[11]
F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems, Variational inequalities and complementarity problems, Proc. Internat. School, Erice, (1978), 151-186, Wiley, Chichester (1980)
-
[12]
X.-X. Huang, J.-C. Yao, Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems, J. Global Optim., 55 (2013), 611--625
-
[13]
V. Jeyakumar, X.-Q. Yang, On characterizing the solution sets of pseudolinear programs, J. Optim. Theory Appl., 87 (1995), 745--755
-
[14]
A. Latif, L.-C. Ceng, S. A. Al-Mezel, Some Iterative Methods for Convergence with Hierarchical Optimization and Variational Inclusions, J. Nonlinear Convex Anal., 17 (2016), 735--755
-
[15]
A. Latif, L.-C. Ceng, Q. H. Ansari, Multi-step hybrid viscosity method for systems of variational inequalities defined over sets of solutions of an equilibrium problem and fixed point problems, Fixed Point Theory and Appl., 2012 (2012), 26 pages
-
[16]
C.-P. Liu, X.-M. Yang, H.-W. Lee, Characterizations of the solution sets of pseudoinvex programs and variational inequalities, J. Inequal. Appl., 2011 (2011), 13 pages
-
[17]
O. L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 7 (1988), 21--26
-
[18]
S. K. Mishra, K. K. Lai, On characterization of solution sets of nonsmooth pseudoinvex minimization problems, International Joint Conference on Computational Sciences and Optimization (CSO), Los Alamitos, (2009), IEEE Comput. Soc., 2 (2009), 739--741
-
[19]
S. R. Mohan, S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901--908
-
[20]
B. S. Mordukhovich, Maximum principle in the problem of time optimal response with nonsmooth constraints, (Russian), translated from Prikl. Mat. Meh., 40 (1976), 1014-1023, J. Appl. Math. Mech., 40 (1976), 960--969
-
[21]
B. S. Mordukhovich, Variational analysis and generalized differentiation, Basic theory, Grundlehren der Math- ematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (2006)
-
[22]
S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475--488
-
[23]
M. Oveisiha, J. Zafarani, Super efficient solutions for set-valued maps, Optimization, 62 (2013), 817--834
-
[24]
M. Oveisiha, J. Zafarani, On characterization of solution sets of set-valued pseudoinvex optimization problems, J. Optim. Theory Appl., 163 (2014), 387--398
-
[25]
M. Rezaie, J. Zafarani, Vector optimization and variational-like inequalities, J. Global Optim., 43 (2009), 47--66
-
[26]
L. B. Santos, M. Rojas-Medar, G. Ruiz-Garzón, A. Rufión-Lizana, Existence of weakly efficient solutions in nonsmooth vector optimization, Appl. Math. Comput., 200 (2008), 547--556
-
[27]
X. M. Yang, On characterizing the solution sets of pseudoinvex extremum problems, J. Optim. Theory Appl., 140 (2009), 537--542
-
[28]
L.-C. Zeng, J.-C. Yao, An existence result for generalized vector equilibrium problems without pseudomonotonicity, Appl. Math. Lett., 19 (2006), 1320--1326
-
[29]
L.-C. Zeng, J.-C. Yao, Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces, J. Global Optim., 36 (2006), 483--497
-
[30]
L.-C. Zeng, J.-C. Yao, Generalized Minty's lemma for generalized vector equilibrium problems, Appl. Math. Lett., 20 (2007), 32--37
-
[31]
K. Q. Zhao, X. Wan, X. M. Yang, A note on characterizing solution set of nonsmooth pseudoinvex optimization problem, Optim. Lett., 7 (2013), 117--126
-
[32]
K. Q. Zhao, X. M. Yang, Characterizations of the solution set for a class of nonsmooth optimization problems, Optim. Lett., 7 (2013), 685--694