In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is ...In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.展开更多
近期,夏远梅等(重庆师范大学(自然科学版),2015,32(1):12-15)利用Δ函数通过非线性标量化方法研究了向量优化问题的∈-真有效解并举例说明了主要结果.笔者指出:其定理1是Gao等(Journal of Industrial and Management Optimization,2011,...近期,夏远梅等(重庆师范大学(自然科学版),2015,32(1):12-15)利用Δ函数通过非线性标量化方法研究了向量优化问题的∈-真有效解并举例说明了主要结果.笔者指出:其定理1是Gao等(Journal of Industrial and Management Optimization,2011,7(2):483-496)建立的定理4.6(i)的特例;其定理2的证明存在不足.通过研究一般的(C,ε)-真有效解的Δ函数非线性标量化,给出了定理2的严谨证明.最后,在∈-真有效解存在的情况下举例说明了主要结果.展开更多
文摘In this paper, we consider a method of centers for solving multi-objective programming problems, where the objective functions involved are concave functions and the set of feasible points is convex. The algorithm is defined so that the sub-problems that must be solved during its execution may be solved by finite-step procedures. Conditions are given under which the algorithm generates sequences of feasible points and constraint multiplier vectors that have accumulation points satisfying the KKT conditions. Finally, we establish convergence of the proposed method of centers algorithm for solving multiobjective programming problems.
文摘近期,夏远梅等(重庆师范大学(自然科学版),2015,32(1):12-15)利用Δ函数通过非线性标量化方法研究了向量优化问题的∈-真有效解并举例说明了主要结果.笔者指出:其定理1是Gao等(Journal of Industrial and Management Optimization,2011,7(2):483-496)建立的定理4.6(i)的特例;其定理2的证明存在不足.通过研究一般的(C,ε)-真有效解的Δ函数非线性标量化,给出了定理2的严谨证明.最后,在∈-真有效解存在的情况下举例说明了主要结果.
