A modified objective function method for solving nonlinear multiobjective fractional programming problems |
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Authors: | Tadeusz Antczak |
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Institution: | Faculty of Mathematics, University of ?ód?, Banacha 22, 90-238 ?ód?, Poland |
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Abstract: | 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. |
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Keywords: | Multiobjective fractional programming problem (Weak) Pareto optimal solution Vector-valued modified Lagrange function Modified vector-valued saddle point V-invex function with respect to η |
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