In this article,we use the robust optimization approach(also called the worst-case approach)for findingε-efficient solutions of the robust multiobjective optimization problem defined as a robust(worst-case)counterpar...In this article,we use the robust optimization approach(also called the worst-case approach)for findingε-efficient solutions of the robust multiobjective optimization problem defined as a robust(worst-case)counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions.Namely,we establish both necessary and sufficient optimality conditions for a feasible solution to be anε-efficient solution(an approximate efficient solution)of the considered robust multiobjective optimization problem.We also use a scalarizing method in proving these optimality conditions.展开更多
In this paper, we first generalize Gerstewitz's functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order pr...In this paper, we first generalize Gerstewitz's functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle.J. Math. Anal. Appl., 419, 904–937(2014)]. By using the generalized Gerstewitz's functions and the partial order principle, we obtain a vector EVP for-efficient solutions in the sense of N′emeth, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.展开更多
基金The research of Yogendra Pandey and Vinay Singh are supported by the Science and Engineering Research Board,a statutory body of the Department of Science and Technology(DST),Government of India,through file no.PDF/2016/001113 and SCIENCE&ENGINEERING RESEARCH BOARD(SERB-DST)through project reference no.EMR/2016/002756,respectively.
文摘In this article,we use the robust optimization approach(also called the worst-case approach)for findingε-efficient solutions of the robust multiobjective optimization problem defined as a robust(worst-case)counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions.Namely,we establish both necessary and sufficient optimality conditions for a feasible solution to be anε-efficient solution(an approximate efficient solution)of the considered robust multiobjective optimization problem.We also use a scalarizing method in proving these optimality conditions.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11471236 and 11561049)
文摘In this paper, we first generalize Gerstewitz's functions from a single positive vector to a subset of the positive cone. Then, we establish a partial order principle, which is indeed a variant of the pre-order principle [Qiu, J. H.: A pre-order principle and set-valued Ekeland variational principle.J. Math. Anal. Appl., 419, 904–937(2014)]. By using the generalized Gerstewitz's functions and the partial order principle, we obtain a vector EVP for-efficient solutions in the sense of N′emeth, which essentially improves the earlier results by completely removing a usual assumption for boundedness of the objective function. From this, we also deduce several special vector EVPs, which improve and generalize the related known results.
