带多面体控制锥的锥约束凸向量优化问题的有效解集的非空有界性的刻画(英文)

本文刻画了控制锥为多面凸锥的锥约束凸向量优化问题有效解集的非空有界性.然后将其中的一个重要条件应用于一类罚函数方法收敛性的研究.     

带多面体控制锥的锥约束凸向量优化问题的有效解集的非空有界性的刻画

本文刻画了控制锥为多面凸锥的锥约束凸向量优化问题有效解集的非空有界性．然后将其中的一个重要条件应用于一类罚函数方法收敛性的研究．     

自反Banach空间中的约束凸向量优化问题的弱有效解集的非空有界性的刻画

本文首先研究无限维自反Banach空间中的锥约束凸向量优化问题的弱有效解集的非空有界性的各种刻画.然后将获得的结果用于研究一类罚函数方法的收敛性.     

Characterizations of the Nonemptiness and Compactness of Solution Sets in Convex Vector Optimization

In this paper, various necessary and sufficient conditions are given for the nonemptiness and compactness of the weakly efficient solution set of a convex vector optimization problem.     

二层多目标最优化问题解集的连通性

研究了二层多目标最优化模型(BLMOP)解集的连通性问题,其中(BLMOP)的上层集值目标函数由下层问题的有效点确定.把(BLMOP)看作成单层的集值函数优化问题,借助集值函数优化问题各种有效解集的连通性的结论,得到了(BLMOP)相应的有效解集连通性的结论.     

Characterization of the Nonemptiness and Compactness of Solution Sets in Convex and Nonconvex Vector Optimization

As a consequence of an abstract theorem proved elsewhere, a vector Weierstrass theorem for the existence of a weakly efficient solution without any convexity assumption is established. By using the notion (recently introduced in an earlier paper) of semistrict quasiconvexity for vector functions and assuming additional structure on the space, new existence results encompassing many results appearing in the literature are derived. Also, when the cone defining the preference relation satisfies some mild assumptions (but including the polyhedral and icecream cones), various characterizations for the nonemptiness and compactness of the weakly efficient solution set to convex vector optimization problems are given. Similar results for a class of nonconvex problems on the real line are established as well.Research supported in part by Conicyt-Chile through FONDECYT 104-0610 and FONDAP-Matemáticas Aplicadas II.     

多目标最优化G-恰当有效解集的存在性和连通性

本文证明了非空紧凸集上拟凸多目标最优化问题的G-恰当有效解的存在性．在此基础上，得到了向量目标函数既是似凸又是拟凸的多目标最优化问题的G-恰当有效解集是连通的结论．同时，还给出一个关于Pareto有效解集连通性的新结果．     

向量优化问题弱有效解集的非空性和紧性刻画

考虑有限维空间Rn(n＞1)中目标映射是仿凸锥映射的向量优化问题.通过对偶锥的端方向和标量函数的0-强制性给出了弱有效解集非空性和紧性的刻画.     

自反Banach空间中向量优化问题弱有效解集特性的进一步研究

本文分别研究了在无限维自反Banach空间中,当控制结构为多面体锥时,-般凸向量优化问题和锥约束凸向量优化问题的弱有效解集的非空有界性,并且把结论应用到了一类罚函数方法的收敛性分析上.     

Nonemptiness and Compactness of Solution Sets to Weakly Homogeneous Generalized Variational Inequalities

Journal of Optimization Theory and Applications - In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special...     

Existence and Boundedness of the Kuhn-Tucker Multipliers in Nonsmooth Multiobjective Optimization

Using the idea of upper convexificators, we propose constraint qualifications and study existence and boundedness of the Kuhn-Tucker multipliers for a nonsmooth multiobjective optimization problem with inequality constraints and an arbitrary set constraint. We show that, at locally weak efficient solutions where the objective and constraint functions are locally Lipschitz, the constraint qualifications are necessary and sufficient conditions for the Kuhn-Tucker multiplier sets to be nonempty and bounded under certain semiregularity assumptions on the upper convexificators of the functions.     

一类锥约束凸向量优化问题弱有效解集非空紧性的刻画和应用

本文研究当目标空间的控制结构为多面体锥时,锥约束凸向量优化问题的弱有效解集的非空紧性的刻画,然后将所获结果用于研究一类罚函数方法的收敛性.     

多目标规划的圆锥有效解

本文利用有限维向量空间中圆锥的概念,引入了多目标规划问题的一种新的有效解－圆锥有效解,并讨论了这种有效解的性质。同时,讲座了圆锥有效解与Pareto有效解以及绝对最优解之间的关系。最后,通过引进目标总值差异概念,分析了圆锥有效解的主要特点。     

Algebra of Efficient Sets for Multiobjective Complex Systems

Complex systems are modeled as collections of multiobjective programs representing interacting subsystems of the overall system. Since the calculation of efficient sets of these complex systems is challenging, it is desirable to decompose the overall system into component multiobjective programs, that are more easily solved and then construct the efficient set of the overall system. For some classes of complex systems, algebraic properties of set operations and relations are developed between the efficient set of the overall system and the efficient sets of subproblems. The properties indicate that multiple decomposition and coordination schemes, with varying assumptions regarding the system, may be applied to the same initial system.     

拓扑空间中锥拟凸映射多目标优化问题有效解集的连通性

本文研究拓扑空间中锥拟凸多目标优化问题的有效解集的连通性．在目标映射是上连续和拟凸(次严格拟凸)的条件下，证明了锥弱有效(有效)解集是连通的.进一步，在是连续和强拟凸的条件下，证明了锥有效解集是路连通的.     

Convergence Results for Henig Proper Efficient Solution Sets of Vector Optimization Problems

In this article, we discuss the convergence of Henig proper minimal point sets and Henig proper efficient solution sets for (strict) proper quasi-convex vector optimization problems when the data of the perturbed problems converges to the data of the original problem in the sense of Painlevé-Kuratowski. Our main results are new and different from those in the literature.     

多目标规划锥有效解的最优性条件

该文提出了广义锥凸向量函数以及向量函数关于锥八的下降、不变、非升、非降方向集等概念．在讨论它们的性质和判别条件的基础上，给出了决策可行集中的点为锥八一有效解的一系列充分必要条件．     

Separations and Optimality of Constrained Multiobjective Optimization via Improvement Sets

In this paper, we investigate the separations and optimality conditions for the optimal solution defined by the improvement set of a constrained multiobjective optimization problem. We introduce a vector-valued regular weak separation function and a scalar weak separation function via a nonlinear scalarization function defined in terms of an improvement set. The nonlinear separation between the image of the multiobjective optimization problem and an improvement set in the image space is established by the scalar weak separation function. Saddle point type optimality conditions for the optimal solution of the multiobjective optimization problem are established, respectively, by the nonlinear and linear separation methods. We also obtain the relationships between the optimal solution and approximate efficient solution of the multiobjective optimization problem. Finally, sufficient and necessary conditions for the (regular) linear separation between the approximate image of the multiobjective optimization problem and a convex cone are also presented.     

Efficient Solution Concepts and Their Relations in Stochastic Multiobjective Programming

In this work, different concepts of efficient solutions to problems of stochastic multiple-objective programming are analyzed. We center our interest on problems in which some of the objective functions depend on random parameters. The existence of different concepts of efficiency for one single stochastic problem, such as expected-value efficiency, minimum-risk efficiency, etc., raises the question of their quality. Starting from this idea, we establish some relationships between the different concepts. Our study enables us to determine what type of efficient solutions are obtained by each of these concepts.     

An Efficient Sampling Approach to Multiobjective Optimization

This paper presents a new approach to multiobjective optimization based on the principles of probabilistic uncertainty analysis. At the core of this approach is an efficient nonlinear multiobjective optimization algorithm, Minimizing Number of Single Objective Optimization Problems (MINSOOP), to generate a true representation of the whole Pareto surface. Results show that the computational savings of this new algorithm versus the traditional constraint method increase dramatically when the number of objectives increases. A real world case study of multiobjective optimal design of a best available control technology for Nitrogen Oxides (NOx) and Sulfur Oxides (SOx) reduction illustrates the usefulness of this approach.