In the paper, a family of real Lipschitz functions, called r-invex, which represents a generalization of the notion of invexity is introduced. The principal analytic tool is the generalized gradient of Clarke for Lips...
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In the paper, a family of real Lipschitz functions, called r-invex, which represents a generalization of the notion of invexity is introduced. The principal analytic tool is the generalized gradient of Clarke for Lipschitz functions. Furthermore, under appropriate r-invexity assumptions, necessary optimality conditions of the Slater type and sufficient optimality conditions are obtained for a nonsmooth programming problem. Also some duality results are obtained for such problems.
In this paper, we are concerned with a nonsmooth programming problem with inequality constraints. We obtain an optimality condition for Kuhn-Tucker points to be minimizers. Later on, we present necessary and sufficien...
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In this paper, we are concerned with a nonsmooth programming problem with inequality constraints. We obtain an optimality condition for Kuhn-Tucker points to be minimizers. Later on, we present necessary and sufficient conditions for weak duality between the primal problem and its mixed type dual, which help us to extend some earlier work from the literature. (C) 2009 Elsevier Ltd. All rights reserved.
This paper examines nonsmooth constrained multi-objective optimization problems where the objective function and the constraints are compositions of convex functions, and locally Lipschitz and Gateaux differentiable f...
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This paper examines nonsmooth constrained multi-objective optimization problems where the objective function and the constraints are compositions of convex functions, and locally Lipschitz and Gateaux differentiable functions. Lagrangian necessary conditions, and new sufficient optimality conditions for efficient and properly efficient solutions are presented. Multi-objective duality results are given for convex composite problems which are not necessarily convex programming problems. Applications of the results to new and some special classes of nonlinear programming problems are discussed. A scalarization result and a characterization of the set of all properly efficient solutions for convex composite problems are also discussed under appropriate conditions.
We consider nonsmooth multiobjective programs where the objective function is a fractional composition of invex functions and locally Lipschitz and G teaux differentiable functions. Kuhn-Tucker necessary and sufficien...
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We consider nonsmooth multiobjective programs where the objective function is a fractional composition of invex functions and locally Lipschitz and G teaux differentiable functions. Kuhn-Tucker necessary and sufficient optimality conditions for weakly efficient solutions are presented. We formulate dual problems and establish weak, strong and converse duality theorems for a weakly efficient solution.
The concept of conditional proper efficiency has been incorporated to develop the duality theory for nonsmooth constrained multiobjective optimization problems where the objective functions. and the constraints are co...
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A Lagrange multiplier theorem is established for a nonsmooth constrained multiobjective optimization problems where the objective function and the constraints are compositions of V-invex functions, and locally Lipschi...
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A Lagrange multiplier theorem is established for a nonsmooth constrained multiobjective optimization problems where the objective function and the constraints are compositions of V-invex functions, and locally Lipschitz and Gåteaux differentiable functions. Furthermore, a vector valued Lagrangian is introduced and vector valued saddle point results are presented. A scalarization result and a characterization of the set of all conditionally properly efficient solutions for V-invex composite problems are also discussed under appropriate conditions.
This paper deals with nonsmooth semi-infinite programming problem which in recent years has become an important field of active research in mathematical programming. A semi-infinite programming problem is characterize...
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This paper deals with nonsmooth semi-infinite programming problem which in recent years has become an important field of active research in mathematical programming. A semi-infinite programming problem is characterized by an infinite number of inequality constraints. We formulate Wolfe as well as Mond-Weir type duals for the nonsmooth semi-infinite programming problem and establish weak, strong and strict converse duality theorems relating the problem and the dual problems. To the best of our knowledge such results have not been done till now.
Sufficient optimality conditions and Mond-Weir duality results for a class of nonsmooth minmax programming problems are obtained under V-invexity type assumptions on objective and constraint functions. Applications of...
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Sufficient optimality conditions and Mond-Weir duality results for a class of nonsmooth minmax programming problems are obtained under V-invexity type assumptions on objective and constraint functions. Applications of these results to certain nonsmooth fractional and nonsmooth generalized fractional programming duality are also presented.
We consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given and some results on duality are proved.
We consider a vector optimization problem with functions defined on Banach spaces. A few sufficient optimality conditions are given and some results on duality are proved.
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