Browse > Article
http://dx.doi.org/10.14317/jami.2017.147

OPTIMIZATION PROBLEMS WITH DIFFERENCE OF SET-VALUED MAPS UNDER GENERALIZED CONE CONVEXITY  

DAS, K. (Department of Mathematics, Indian Institute of Technology Kharagpur)
NAHAK, C. (Department of Mathematics, Indian Institute of Technology Kharagpur)
Publication Information
Journal of applied mathematics & informatics / v.35, no.1_2, 2017 , pp. 147-163 More about this Journal
Abstract
In this paper, we establish the necessary and sufficient Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with difference of set-valued maps under generalized cone convexity assumptions. We also study the duality results of Mond-Weir (MW D), Wolfe (W D) and mixed (Mix D) types for the weak solutions of the problem (P).
Keywords
Convex cone; set-valued map; cone convexity; duality;
Citations & Related Records
연도 인용수 순위
  • Reference
1 J. Baier and J. Jahn, On subdifferentials of set-valued maps, J. Optim. Theory Appl. Vol. 100 (1999), 233-240.   DOI
2 J. Borwein, Multivalued convexity and optimization: a unified approach to inequality and equality constraints, Math. Program. 13 (1977), 183-199.   DOI
3 J.M. Borwein, A lagrange multiplier theorem and a sandwich theorem for convex relations, Math. Scand. 48 (1981), 189-204.   DOI
4 K. Das and C. Nahak, Sufficient optimality conditions and duality theorems for set-valued optimization problem under generalized cone convexity, Rend. Circ. Mat. Palermo (1952-) 63 (2014), 329-345.   DOI
5 K. Das and C. Nahak, Sufficiency and duality of set-valued optimization problems via higher-order contingent derivative, J. Adv. Math. Stud. 8 (2015), 137-151.
6 K. Das and C. Nahak, Set-valued fractional programming problems under generalized cone convexity, Opsearch 53 (2016), 157-177.   DOI
7 F. Flores-Bazan and W. Oettli, Simplified optimality conditions for minimizing the difference of vector-valued functions, J. Optim. Theory Appl. 108 (2001), 571-586.   DOI
8 N. Gadhi, Optimality conditions for the difference of convex set-valued mappings, Positivity 9 (2005), 687-703.   DOI
9 N. Gadhi, M. Laghdir and A. Metrane, Optimality conditions for D:C: vector optimization problems under reverse convex constraints, J. Glob. Optim. 33 (2005), 527-540.   DOI
10 N. Gadhi, A. Metrane, Sufficient optimality condition for vector optimization problems under dc data, J. Glob. Optim. 28 (2004), 55-66.   DOI
11 X.L. Guo, S.J. Li and K.L. Teo, Subdifferential and optimality conditions for the difference of set-valued mappings, Positivity 16 (2012), 321-337.   DOI
12 T. Tanino and Y. Sawaragi, Conjugate maps and duality in multiobjective optimization, J. Optim. Theory Appl. 31 (1980), 473-499.   DOI
13 J.B. Hiriart-Urruty, From convex optimization to nonconvex optimization, in: Clarke, F.H., Demyanov, V.F., Giannessi, F. (eds.) Nonsmooth Optimization and Related Topics, Plenum, New York, 1989, pp. 219-239.
14 L.Lahoussine, A. A. Elhilali and N. Gadhi, Set-valued mapping monotonicity as characterization of D:C: functions, Positivity 13 (2009), 399-405.   DOI
15 A. Taa, Optimality conditions for vector optimization problems of a difference of convex mappings, J. Glob. Optim. 31 (2005), 421-436.   DOI