共查询到20条相似文献,搜索用时 31 毫秒
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In this paper, we introduce a sequential approximate strong Karush–Kuhn–Tucker (ASKKT) condition for a multiobjective optimization problem with inequality constraints. We show that each local efficient solution satisfies the ASKKT condition, but weakly efficient solutions may not satisfy it. Subsequently, we use a so-called cone-continuity regularity (CCR) condition to guarantee that the limit of an ASKKT sequence converges to an SKKT point. Finally, under the appropriate assumptions, we show that the ASKKT condition is also a sufficient condition of properly efficient points for convex multiobjective optimization problems. 相似文献
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首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。 相似文献
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首先,举例验证了三种D-η-半预不变真拟凸映射的存在性;然后,在D-η-半严格(严格)半预不变真拟凸性下,得出了多目标优化问题的局部有效解为全局有效解,局部弱有效解为全局弱有效解,并举例验证了所得结果;最后,在D-η-严格半预不变真拟凸性下,建立了多目标优化问题的全局弱有效解和局部弱有效解的唯一性的刻画。 相似文献
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Shouyang Wang 《Applied Mathematics Letters》1991,4(6):91-93
In this short paper, we give a result on scalarization of multiobjective optimization. Any local weakly efficient solution of a multiobjective programming problem is a locally optimal solution of the corresponding weighted optimization problem if and only if one of the three conditions proposed in this paper is satisfied. 相似文献
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E. Miglierina 《Rendiconti del Circolo Matematico di Palermo》2001,50(1):153-164
A characterization of weakly efficient, efficient and properly efficient solutions of multiobjective optimization problems
is given in terms of a scalar optimization problem by using a special “distance” function. The concept of the well-posedness
for this special scalar problem is then linked with the properly efficient solutions of the multiobjective problem. 相似文献
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与多目标规划问题的G恰当有效解相应,引进了集合的G恰当有效点的概念,并互研究了G恰当有效点集和G恰当有效解集的连通性.利用所得的结果,还获得多目标规划问题的Pareto有效解集是连通的一个新的结论。 相似文献
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序扰动多目标规划的锥次微分稳定性 总被引:9,自引:1,他引:8
对于局部凸拓扑向量空间的多目标规划问题,本文研究并得到当确定空间序的控制锥受扰动,它们的锥有效点(解)集和锥弱有效点(解)集分别在锥次微分和锥弱次微分意义下的稳定性结果. 相似文献
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F. Lara 《Optimization》2017,66(8):1259-1272
In this paper, we use generalized asymptotic functions and second-order asymptotic cones to develop a general existence result for the nonemptiness of the proper efficient solution set and a sufficient condition for the domination property in nonconvex multiobjective optimization problems. A new necessary condition for a point to be efficient or weakly efficient solution is given without any convexity assumption. We also provide a finer outer estimate for the asymptotic cone of the weakly efficient solution set in the quasiconvex case. Finally, we apply our results to the linear fractional multiobjective optimization problem. 相似文献
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本文引进Banach空间中的ε-扩展集和ε-扩展锥概念.借助ε-扩展锥,定义了多目标规划问题的ε-恰当有效解和局部ε-恰当有效解,并且研究了这些解的性质.此外还讨论了ε-恰当有效解与某些其它恰当有效解的关系. 相似文献
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S. K. Zhu 《Optimization Letters》2016,10(6):1287-1301
By using the generalized Fermat rule, the Mordukhovich subdifferential for maximum functions, the fuzzy sum rule for Fréchet subdifferentials and the sum rule for Mordukhovich subdifferentials, we establish a necessary optimality condition for the local weak sharp efficient solution of a constrained multiobjective optimization problem. Moreover, by employing the approximate projection theorem, and some appropriate convexity and affineness conditions, we also obtain some sufficient optimality conditions respectively for the local and global weak sharp efficient solutions of such a multiobjective optimization problem. 相似文献
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约束锥扰动多目标规划锥有效解集的闭性和半连续性 总被引:4,自引:0,他引:4
本文研究拓扑向量空间中目标映射和约束映射均为连续,约束映射的约束锥为半连续的条件下,受扰动可达目标集的锥有效点集和锥弱有效点集的闭性、半连续性和锥半连续性.在此基础上,得到了约束锥扰动多目标规划问题的锥有效解集和锥弱有效解集的闭性和半连续性. 相似文献
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J.Y. Bello Cruz L.R. Lucambio Pérez J.G. Melo 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(16):5268-5273
We consider the projected gradient method for solving the problem of finding a Pareto optimum of a quasiconvex multiobjective function. We show convergence of the sequence generated by the algorithm to a stationary point. Furthermore, when the components of the multiobjective function are pseudoconvex, we obtain that the generated sequence converges to a weakly efficient solution. 相似文献
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一类G-(F,ρ)凸多目标分式规划的最优性条件 总被引:1,自引:0,他引:1
本文讨论了一类多目标分式规划问题,其中所包含的函数是局部Lipschitz的和Clarke次可微的.首先,在G-(F,ρ)凸的条件下,证明了择一定理.然后,证明了该多目标分式规划问题在Geoffrion意义下的真有效解的充分条件和必要条件. 相似文献
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Pham Huu Sach 《Numerical Functional Analysis & Optimization》2013,34(3-4):371-392
In this paper, we consider some dual problems of a primal multiobjective problem involving nonconvex set-valued maps. For each dual problem, we give conditions under which strong duality between the primal and dual problems holds in the sense that, starting from a Benson properly efficient solution of the primal problem, we can construct a Benson properly efficient solution of the dual problem such that the corresponding objective values of both problems are equal. The notion of generalized convexity of set-valued maps we use in this paper is that of near-subconvexlikeness. 相似文献
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In this paper, nonconvex multiobjective optimization problems are studied. New characterizations of a properly efficient solution in the sense of Geoffrion's are established in terms of the stability of one scalar optimization problem and the existence of an exact penalty function of a scalar constrained program, respectively. One of the characterizations is applied to derive necessary conditions for a properly efficient control-parameter pair of a nonconvex multiobjective discrete optimal control problem with linear constraints. 相似文献
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