Optimality conditions and duality in nonsmooth multiobjective optimization problems

被引：0
作者：
Thai Doan Chuong
Do Sang Kim
机构：
[1] Saigon University,Department of Mathematics & Applications
[2] Pukyong National University,Department of Applied Mathematics
来源：
Annals of Operations Research | 2014年 / 217卷
关键词：
Optimality condition; Duality; The (KKT) condition; Limiting subdifferential; -invex-infine function; Multiobjective optimization; 49K99; 65K10; 90C29; 90C46;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Exploiting some tools of modern variational analysis involving the approximate extremal principle, the fuzzy sum rule for the Fréchet subdifferential, the sum rule for the limiting subdifferential and the scalarization formulae of the coderivatives, we establish necessary conditions for (weakly) efficient solutions of a multiobjective optimization problem with inequality and equality constraints. Sufficient conditions for (weakly) efficient solutions of an aforesaid problem are also provided by means of employing L-(strictly) invex-infine functions defined in terms of the limiting subdifferential. In addition, we introduce types of Wolfe and Mond–Weir dual problems and investigate weak/strong duality relations.
引用
收藏
页码：117 / 136
页数：19
相关论文
共 44 条
[1]  
Antczak T.(2006)An η-approximation approach in nonlinear vector optimization with univex functions The Asia-Pacific Journal of Operational Research 23 525-542
[2]  
Antczak T.(2009)Optimality conditions and duality for nondifferentiable multiobjective programming problems involving d-r-type I functions The Journal of Computational and Applied Mathematics 225 236-250
[3]  
Askar S. S.(2009)First-order optimality conditions and duality results for multi-objective optimisation problems Annals of Operations Research 172 277-289
[4]  
Tiwari A.(2004)Regularity conditions and optimality in vector optimization Numerical Functional Analysis and Optimization 25 479-501
[5]  
Chandra S.(2007)Optimality conditions and duality for nondifferentiable multiobjective fractional programming with generalized convexity Annals of Operations Research 154 133-147
[6]  
Dutta J.(2012)-invex-infine functions and applications Nonlinear Analysis 75 5044-5052
[7]  
Lalitha C. S.(2013)Optimality and duality for proper and isolated efficiencies in multiobjective optimization Nonlinear Analysis 76 93-104
[8]  
Chinchuluun A.(1993)Convex composite multi-objective nonsmooth programming Mathematical Programming Series A 59 325-343
[9]  
Yuan D.(2008)Pseudoinvexity, optimality conditions and efficiency in multiobjective problems; duality Nonlinear Analysis 68 24-34
[10]  
Pardalos P. M.(2010)A characterization of pseudoinvexity for the efficiency in nondifferentiable multiobjective problems. Duality Nonlinear Analysis 73 1109-1117
12345