DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR ROBUST MULTIOBJECTIVE OPTIMIZATION PROBLEMS
DUALITY THEOREM AND VECTOR SADDLE POINT THEOREM FOR ROBUST MULTIOBJECTIVE OPTIMIZATION PROBLEMS
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DOI：
10.4134/ckms.2013.28.3.597
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发表时间：
2013-07
影响因子：
0.6
通讯作者：
M. Kim
中科院分区：
文献类型：
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作者：
M. Kim
摘要。本文在广义指数假设下，给出了一类不确定多目标鲁棒优化问题的Mond-Weir对偶性结果。在凸性假设下，得到了弱向量鞍点定理。1. 考虑一个不确定多目标鲁棒优化问题：（MRP）最小化(f1 (x)，…∀v j∈v j, j = 1，…，m，其中vi是不确定参数，vi∈vi，对于rq中的某个凸紧集tv i， if i: rn→R, i = 1，…，l, g j: R n × R q→R, j = 1，…，m是连续可微的。当l = 1时，（MRP）变成了一个不确定优化问题，这在（[4]-[5],[6]）中已被深入研究，它与不确定程序（UP）的鲁棒对应[1]相关联，（RP） inf∈rn {f(x): gi (x, v1)≤0,∀v1∈v1, i = 1，…，m}，其中参数在其规定的不确定性集合vi， i = 1，…，m内的每个可能值都强制执行不确定性约束。最近，Jeyakumar， Li和Lee等人建立了面向数据不确定性的广义凸规划问题的鲁棒对偶理论。此外，Kim[8]推广了Jeyakumar、Li和Lee[7]针对不确定多目标鲁棒优化问题的结果。本文给出了一类不确定多目标鲁棒优化问题的Mond-Weir对偶性结果
Abstract. In this paper, Mond-Weir type duality results for a uncertainmultiobjective robust optimization problem are given under generalizedinvexity assumptions. Also, weak vector saddle-point theorems are ob-tained under convexity assumptions. 1. IntroductionConsider an uncertain multiobjective robust optimization problem:(MRP) minimize (f 1 (x),...,f l (x))subject to g j (x,v j ) <= 0, ∀v j ∈ V j , j = 1,...,m,where v i is an uncertain parameter and v i ∈ V i for some convex compact setV i in R q , f i : R n → R, i = 1,...,l and g j : R n × R q → R, j = 1,...,m arecontinuously differentiable.When l = 1, (MRP) becomes an uncertain optimization problem, which hasbeen intensively studied in ([4]-[5], [6]), associates with the uncertain program(UP) its robust counterpart [1],(RP) inf x∈R n {f(x) : g i (x,v i ) ≤ 0, ∀v i ∈ V i , i = 1,...,m},where the uncertain constraints are enforced for every possible value of theparameters within their prescribed uncertainty sets V i , i = 1,...,m. Recently,Jeyakumar, Li and Lee [7] established a robust duality theory for generalizedconvex programming problems in the face of data uncertainty. Furthermore,Kim [8] extended results of Jeyakumar, Li and Lee [7] for a uncertain multi-objective robust optimization problem. In this paper, Mond-Weir type dualityresults for a uncertain multiobjective robust optimization problem are given