The concept of mixed-type duality has been extended to the class of multiobjective variational problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual...
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The concept of mixed-type duality has been extended to the class of multiobjective variational problems. A number of duality relations are proved to relate the efficient solutions of the primal and its mixed-type dual problems. The results are obtained for rho -convex (generalized rho -convex) functions. These studies have been generalized to the case of rho -invex (generalized rho -invex) functions. Our results apparently generalize a fairly large number of duality results previously obtained for finite-dimensional nonlinear programming problems under various convexity assumptions. (C) 2000 Academic Press.
Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded un...
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Hanson and Mond have grven sets of necessary and sufficient conditions for optimality in constrained optimization by introducing classes of generalized functions, called type Ⅰ functions. Recently, Bector definded univex functions, a new class of functions that unifies several concepts of generalized convexity. In this paper, additional conditions are attached to the Kuhn Tucker conditions giving a set of conditions which are both necessary and sufficient for optimality in constrained optimization, under appropriate constraint qualifications.
An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and s...
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The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability...
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The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective programming problem under two perturbations are obtained in Banach space.
We suggest the second-order symmetric and self dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong, and converse duality theorems under conv...
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We suggest the second-order symmetric and self dual programs in multiobjective nonlinear programming. For these second-order symmetric dual programs, we prove the weak, strong, and converse duality theorems under convexity and concavity conditions. Also, we prove the self duality theorem for these second-order self dual programs and illustrate its example.
In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A cou...
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In this paper, three sufficient conditions are given, one of which modifies the previous result given by Singh (Ref. 1) under the assumption of convexity of the functions involved at the Pareto-optimal solution. A counterexample has been furnished which shows that the convexity assumption cannot be extended to include the quasiconvexity case. The second theorem on sufficiency requires the strict pseudoconvexity of the functions involved.
The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability...
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The stability in the sense of semicontinuation for the cone efficient points and the cone weakly efficient points of a perturbation set in Banach space with perturbation order are studied. On this basis, the stability for the cone efficient solutions and the cone weakly efficient solutions of multiobjective programming problem under two perturbations are obtained in Banach space.
Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be sufficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. D...
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Necessary conditions for optimality in multiobjective programming involving subdifferentiable set functions are shown to be sufficient under the assumption of a particular form of ρ-convexity or ρ-pseudoconvexity. Duality results are thus extended for a Wolfe-type or a Mond-Weir type dual.
This paper provides a methodology for the optimization of an existing electrical distribution network when upgraded by renewable energies. The contribution of renewable energy in electricity generation is decided upon...
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This paper provides a methodology for the optimization of an existing electrical distribution network when upgraded by renewable energies. The contribution of renewable energy in electricity generation is decided upon through both network design optimization and proper load management whereby applications that can be satisfied by non-electrical means are separated from the main load. The remaining load will then be satisfied by an optimal mix of renewable energy which will be injected to the existing grid. The proposed problem will be formulated using multiobjective linear programming in conjunction with fuzzy logic. It will be shown that optimization using fuzzy logic can provide decision makers with more flexibility that would assist them in the allocation of various energy resources to optimally meet the various end uses and solve the problem of renewable energy connection to existing distribution networks. Copyright (C) 1999 John Wiley & Sons, Ltd.
The problem of determining nondominated schedules to take buses from depots to the starting points of their routes, spare capacity and the number of buses to be parked overnight at each depot is considered with two ob...
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The problem of determining nondominated schedules to take buses from depots to the starting points of their routes, spare capacity and the number of buses to be parked overnight at each depot is considered with two objectives without assigning priorities to them. The two objectives are to minimize the cumulative distance covered by all the buses and the maximum distance among the distances covered by individual buses from the depots to the starting points of their respective routes. An algorithm is developed to obtain the set of nondominated solutions of this two-objective problem. (C) 1999 Elsevier Science B.V. All rights reserved.
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