This paper deals with multiobjective programming problems with support functions under(G, C, ρ)-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective prog...
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This paper deals with multiobjective programming problems with support functions under(G, C, ρ)-convexity assumptions. Not only sufficient but also necessary optimality conditions for this kind of multiobjective programming problems are established from a viewpoint of(G, C, ρ)-*** the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.
In this paper, we deal with multiobjective programming problems involving functions which are not necessarily differential. A new concept of generalized convexity, which is called (G, C, rho)-convexity, is introduced....
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In this paper, we deal with multiobjective programming problems involving functions which are not necessarily differential. A new concept of generalized convexity, which is called (G, C, rho)-convexity, is introduced. We establish not only sufficient but also necessary optimality conditions for multiobjective programming problems from a viewpoint of the new generalized convexity. When the sufficient conditions are utilized, the corresponding duality theorems are derived for general Mond-Weir type dual program.
In this paper, we employ advanced techniques of variational analysis and generalized differentiation to examine robust optimality conditions and robust duality for an uncertain nonsmooth multiobjective optimization pr...
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In this paper, we employ advanced techniques of variational analysis and generalized differentiation to examine robust optimality conditions and robust duality for an uncertain nonsmooth multiobjective optimization problem under arbitrary uncertainty nonempty sets. We establish necessary and sufficient optimality conditions for (local) robust (weakly) efficient solutions of the considered problem. Our problem involves nonsmooth real-valued functions and data uncertainty in both the objective and constraint functions, and its necessary and sufficient optimality conditions are exhibited in terms of multipliers and the Mordukhovich or Clarke subdifferentials of the related functions. Moreover, we formulate a dual multiobjective problem to the underlying program and examine robust weak, strong, and converse duality relations between the primal problem and its dual under assumptions of (strictly) generalized convexity.
This paper studies the stability for bilevel program where the lower-level program is a multiobjective programming problem. As we know, the weakly efficient solution mapping for parametric multiobjective program is no...
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This paper studies the stability for bilevel program where the lower-level program is a multiobjective programming problem. As we know, the weakly efficient solution mapping for parametric multiobjective program is not generally lower semicontinuous. We first obtain this semicontinuity under a suitable assumption. Then, a new condition for the lower semicontinuity of the efficient solution mapping of this problem is also obtained. Finally, we get the continuities of the value functions and the solution set mapping for the upper-level problem based on the semicontinuities of solution mappings for the lower-level parametric multiobjective program.
We introduce and characterize a class of differentiable convex functions for which the Karush-Kuhn-Tucker condition is necessary for optimality. If some constraints do not belong to this class, then the characterizati...
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We introduce and characterize a class of differentiable convex functions for which the Karush-Kuhn-Tucker condition is necessary for optimality. If some constraints do not belong to this class, then the characterization of optimality generally assumes an asymptotic form. We also show that for the functions that belong to this class in multi-objective optimization, Pareto solutions coincide with strong Pareto solutions,. This extends a result, well known for the linear case.
In this paper, we consider a convex quadratic multiobjective optimization problem, where both the objective and constraint functions involve data uncertainty. We employ a deterministic approach to examine robust optim...
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In this paper, we consider a convex quadratic multiobjective optimization problem, where both the objective and constraint functions involve data uncertainty. We employ a deterministic approach to examine robust optimality conditions and find robust (weak) Pareto solutions of the underlying uncertain multiobjective problem. We first present new necessary and sufficient conditions in terms of linear matrix inequalities for robust (weak) Pareto optimality of the multiobjective optimization problem. We then show that the obtained optimality conditions can be alternatively checked via other verifiable criteria including a robust Karush-Kuhn-Tucker condition. Moreover, we establish that a (scalar) relaxation problem of a robust weighted-sum optimization program of the multiobjective problem can be solved by using a semidefinite programming (SDP) problem. This provides us with a way to numerically calculate a robust (weak) Pareto solution of the uncertain multiobjective problem as an SDP problem that can be implemented using, e.g., MATLAB.
We formulate the Wolfe, Mond-Weir and generalized Mond-Weir types of dual problems for a multiobjec-tive program involving vector valued n-set functions. By using the concept of efficiency (Pareto optimum) we prove th...
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The sensitivity of a convex noniinear constrained multiobjective program to small perturbations is analysed, in terms of the stability of weak optimal faces, and vertices, to perturbations. These results are applied t...
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The sensitivity of a convex noniinear constrained multiobjective program to small perturbations is analysed, in terms of the stability of weak optimal faces, and vertices, to perturbations. These results are applied to the perturbation of a set-valued optimization problem, in which the objective and constraint set-functions take convex poiyhedra as their values
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