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1.
The concept of efficiency is used to formulate duality for nondifferentiable multiobjective variational problems. Wolfe and Mond-Weir type vector dual problems are formulated. By using the generalized Schwarz inequality and a characterization of efficient solution, we established the weak, strong, and converse duality theorems under generalized (F,ρ)-convexity assumptions.  相似文献   

2.
A class of functions called higher-order (F, α, ρ, d)-V-type I functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for higher-order Wolfe and Mond-Weir type multiobjective dual programs in order to relate the efficient solutions of primal and dual problems.  相似文献   

3.
In this work, we consider a new class of multitime multiobjective variational problems of minimizing a vector of functionals of curvilinear integral type. Based on the normal efficiency conditions for multitime multiobjective variational problems, we study duals of Mond-Weir type, generalized Mond-Weir-Zalmai type and under some assumptions of (??, b)-quasiinvexity, duality theorems are stated. We give weak duality theorems, proving that the value of the objective function of the primal cannot exceed the value of the dual. Moreover, we study the connection between values of the objective functions of the primal and dual programs, in direct and converse duality theorems. While the results in §1 and §2 are introductory in nature, to the best of our knowledge, the results in §3 are new and they have not been reported in literature.  相似文献   

4.
The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.   相似文献   

5.
In this paper, we establish characterizations for efficient solutions to multiobjective programming problems, which generalize the characterization of established results for optimal solutions to scalar programming problems. So, we prove that in order for Kuhn–Tucker points to be efficient solutions it is necessary and sufficient that the multiobjective problem functions belong to a new class of functions, which we introduce. Similarly, we obtain characterizations for efficient solutions by using Fritz–John optimality conditions. Some examples are proposed to illustrate these classes of functions and optimality results. We study the dual problem and establish weak, strong and converse duality results.  相似文献   

6.
A new method is used for solving nonlinear multiobjective fractional programming problems having V-invex objective and constraint functions with respect to the same function η. In this approach, an equivalent vector programming problem is constructed by a modification of the objective fractional function in the original nonlinear multiobjective fractional problem. Furthermore, a modified Lagrange function is introduced for a constructed vector optimization problem. By the help of the modified Lagrange function, saddle point results are presented for the original nonlinear fractional programming problem with several ratios. Finally, a Mond-Weir type dual is associated, and weak, strong and converse duality results are established by using the introduced method with a modified function. To obtain these duality results between the original multiobjective fractional programming problem and its original Mond-Weir duals, a modified Mond-Weir vector dual problem with a modified objective function is constructed.  相似文献   

7.
Second order mixed type dual is introduced for multiobjective programming problems. Results about weak duality, strong duality, and strict converse duality are established under generalized second order (F,ρ)-convexity assumptions. These results generalize the duality results recently given by Aghezzaf and Hachimi involving generalized first order (F,ρ)-convexity conditions.  相似文献   

8.
We suggest a pair of second-order symmetric dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong and converse duality theorems under F-convexity conditions.  相似文献   

9.
In this paper, new classes of generalized (F,α,ρ,d)-type I functions are introduced for differentiable multiobjective programming. Based upon these generalized functions, first, we obtain several sufficient optimality conditions for feasible solution to be an efficient or weak efficient solution. Second, we prove weak and strong duality theorems for mixed type duality.  相似文献   

10.
We prove that in order for the Kuhn-Tucker or Fritz John points to be efficient solutions, it is necessary and sufficient that the non-differentiable multiobjective problem functions belong to new classes of functions that we introduce here: KT-pseudoinvex-II or FJ-pseudoinvex-II, respectively. We illustrate it by examples. These characterizations generalize recent results given for the differentiable case. We study the dual problem and establish weak, strong and converse duality results.  相似文献   

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