In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized pr...In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.展开更多
The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U...Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.展开更多
In this paper some optimality criteria are proved and some Mond\|Weir type duality theorem for multiobjective fractional programming problems defined in a Banach space is obtained.
In this paper,we study the connectedness of proper efficient solution sets of the vector optimization problem for a strict cone--quasiconvex mapping in a separated topological linear space.
Using generalized univex functions, a nondifferentiable multiple-objective optimization problem is considered.Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or p...Using generalized univex functions, a nondifferentiable multiple-objective optimization problem is considered.Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Mond-Weir type duality programming is constructed,the weak and strong duality theorems are proved.展开更多
文摘In this article, a novel scalarization technique, called the improved objective-constraint approach, is introduced to find efficient solutions of a given multiobjective programming problem. The presented scalarized problem extends the objective-constraint problem. It is demonstrated that how adding variables to the scalarized problem, can lead to find conditions for (weakly, properly) Pareto optimal solutions. Applying the obtained necessary and sufficient conditions, two algorithms for generating the Pareto front approximation of bi-objective and three-objective programming problems are designed. These algorithms are easy to implement and can achieve an even approximation of (weakly, properly) Pareto optimal solutions. These algorithms can be generalized for optimization problems with more than three criterion functions, too. The effectiveness and capability of the algorithms are demonstrated in test problems.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.
文摘In this paper some optimality criteria are proved and some Mond\|Weir type duality theorem for multiobjective fractional programming problems defined in a Banach space is obtained.
文摘In this paper,we study the connectedness of proper efficient solution sets of the vector optimization problem for a strict cone--quasiconvex mapping in a separated topological linear space.
基金Shandong Science Development Plan Foundation ( NO.JOOP 55)
文摘Using generalized univex functions, a nondifferentiable multiple-objective optimization problem is considered.Kuhn-Tucker type sufficient optimality conditions are obtained for a feasible point to be an efficient or properly efficient solution. Mond-Weir type duality programming is constructed,the weak and strong duality theorems are proved.
