非凸多目标优化中真有效解的一个非线性标量化性质

基于Pascoletti-Serafini标量化方法,利用罚函数思想提出了一类新的标量化函数,进而获得非凸多目标优化问题真有效解的充分条件和必要条件.该结果的建立不需要目标函数的像集有界这一条件,故文章是对Akbari等人[J.Optim.Theory Appl.,2018,178(2):560-590]建立的相应标量...     

向量优化中\varepsilon-真有效解的非线性标量化性质

利用G\"{o}pfert等提出的非线性标量化函数给出了向量优化中\varepsilon-真有效解的一个非线性标量化性质, 并提出几个例子对主要结果进行了解释.     

多目标优化问题拟近似有效解非线性标量化的一个注记

主要研究多目标优化问题拟近似(弱)有效解.在没有任何凸性假设下,通过非线性标量化方法给出了多目标优化问题拟近似(弱)有效解的充分条件.主要结果修正了已有文献中的错误,并通过例子对其错误进行了说明.     

向量优化问题的一类非线性标量化定理

利用Gertewitz泛函研究向量优化问题的一类非线性标量化问题. 证明了向量优化问题的(C, \varepsilon)-弱有效解或(C, \varepsilon)-有效解与标量化问题的近似解或严格近似解间的等价关系, 并估计了标量化问题的近似解．     

一类多目标优化问题的有效性

本文研究了一类带不等式约束的多目标优化问题,给出了该类问题的有效解的一些充分必要条件,在适当条件下利用线性标量化方法证明了其有效解和真有效解的等价性。本文的主要结论是对最近一些文献中相应结果的改进与推广。     

向量优化问题 (C,\varepsilon)-弱有效解的一种非线性标量化性质

Guti\'{e}rrez 等在 co-radiant 集的基础上提出了一种新的 (C,\varepsilon)-弱有效解, 它统一了之前文献中提出的几种经典的近似解. 利用由 G\"{o}pfert 等提出的一类非线性标量化函数, 给出了 (C,\varepsilon)-弱有效解的一个等价性质. 最后, 给出一个例子说明主要结果.     

赋范线性空间多目标规划的 广义KT-真有效解

对于赋范线性空间中的多目标规划问题,引进了广义KT-真有效解的概念.在一定条件下,得到了广义KT-真有效解和广义H-局部真有效解之间的关系.     

多目标优化问题鲁棒有效解与真有效解之间的关系

在一定条件下研究了多目标优化问题鲁棒有效解与真有效解之间的关系及鲁棒有效解的最优性条件.首先,给出多目标优化问题鲁棒弱有效解的概念,研究它与鲁棒有效解和真有效解之间的关系,举例说明了相关结果的合理性.其次,在次类凸和伪凸性假设下研究了鲁棒有效解的必要性条件和充分性条件.     

多目标优化问题Proximal真有效解的最优性条件

在广义凸性假设下,给出了集合proximal真有效点的线性标量化,并在此基础上证明了它与Benson真有效点和Borwein真有效点的等价性.将这些结果应用到多目标优化问题上,得到proximal真有效解的最优性条件.最后,利用proximal次微分,得到了proximal真有效解的模糊型最优性条件.     

On quadratic scalarization of vector optimization problems in Banach spaces

We study vector optimization problems in partially ordered Banach spaces and suppose that the objective mapping possesses a weakened property of lower semicontinuity and make no assumptions on the interior of the ordering cone. We discuss the so-called adaptive scalarization of such problems and show that the corresponding scalar non-linear optimization problems can be by-turn approximated by quadratic minimization problems.     

Fuzzy optimality conditions for fractional multi-objective problems

In this article, we are concerned with fractional multi-objective optimization problems. Since those problems are in general nonconvex problems even if the problem data are convex, using techniques from variational analysis especially the approximate extremal principle [B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, I: Basic Theory, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 330, Springer, Berlin, 2006; B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, II: Applications, Grundlehren Series: Fundamental Principles of Mathematical Sciences, Vol. 331, Springer, Berlin, 2006], we develop fuzzy optimality conditions.     

多目标最优化恰当有效解的稳定性

主要研究当两种类型的参数扰动时,多目标最优化问题中恰当有效解的稳定性.在点集映射的连续性意义下,分析讨论这种稳定性问题并分别给出引起扰动的两参数u,v所对应的点集映射Q1(u)和Q2(v),同时严格证明了在两个闭凸锥U,V上Q1(u)和Q2(v)的连续性定理.最后,通过附注对其进行补充和改进.     

Robustness to uncertain optimization using scalarization techniques and relations to multiobjective optimization

In this paper, we propose two kinds of robustness concepts by virtue of the scalarization techniques (Benson’s method and elastic constraint method) in multiobjective optimization, which can be characterized as special cases of a general non-linear scalarizing approach. Moreover, we introduce both constrained and unconstrained multiobjective optimization problems and discuss their relations to scalar robust optimization problems. Particularly, optimal solutions of scalar robust optimization problems are weakly efficient solutions for the unconstrained multiobjective optimization problem, and these solutions are efficient under uniqueness assumptions. Two examples are employed to illustrate those results. Finally, the connections between robustness concepts and risk measures in investment decision problems are also revealed.     

Optimality conditions for vector equilibrium problems in normed spaces

By using the concepts of contingent epiderivative, radial epiderivative, Clarke tangent epiderivative and Y-epiderivative, we present necessary and sufficient conditions for the weakly efficient solution, the Henig efficient solution, and the globally proper efficient solution, respectively, to vector equilibrium problems with constraints.     

Necessary and sufficient optimality conditions for fractional multi-objective problems

Using a special scalarization, we give necessary optimality conditions for fractional multiobjective optimization problems. Under a generalized invexity, sufficient optimality conditions are also given. All over the article, the data are assumed to be continuous but not necessarily Lipschitz.     

Nonconvex scalarization in set optimization with set-valued maps

The aim of this work is to obtain scalar representations of set-valued optimization problems without any convexity assumption. Using a criterion of solution introduced by Kuroiwa [D. Kuroiwa, Some duality theorems of set-valued optimization with natural criteria, in: Proceedings of the International Conference on Nonlinear Analysis and Convex Analysis, World Scientific, River Edge, NJ, 1999, pp. 221-228], which is based on ordered relations between sets, we characterize this type of solutions by means of nonlinear scalarization. The scalarizing function is a generalization of the Gerstewitz's nonconvex separation function. As applications of our results we give two existence theorems for set-valued optimization problems.