不确定多目标优化鲁棒真有效解的最优性与对偶

本文研究一类不确定性多目标优化问题鲁棒真有效解的最优性条件和对偶理论.首先,借助鲁棒真有效解的标量化定理,在鲁棒型闭凸锥约束品性下,建立了不确定多目标优化问题真有效解的最优性条件;其次,针对原不确定多目优化的Wolfe型对偶问题,得到关于鲁棒真有效解的强、弱对偶定理.     

非凸多目标优化模型的一类鲁棒逼近最优性条件

通过引入一类非凸多目标不确定优化问题，借助鲁棒优化方法，先建立了该不确定多目标优化问题的鲁棒对应模型；再借助标量化方法和广义次微分性质，刻画了该不确定多目标优化问题的鲁棒拟逼近有效解的最优性条件，推广和改进了相关文献的结论.     

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.     

不确定凸优化问题鲁棒近似解的最优性

该文研究一类目标和约束函数均带有不确定信息的凸优化问题的鲁棒近似解.首先,在闭凸锥约束品性假设下,得到了该不确定优化问题关于近似解的最优性条件.然后,引入所研究不确定优化问题的近似鞍点的概念,并给出了近似解的鞍点刻划.     

鲁棒凸优化问题拟近似解的刻划

本文研究鲁棒凸优化问题拟近似解的最优性条件和对偶理论.首先利用鲁棒优化方法,在由约束函数的共轭函数的上图给出的闭凸锥约束规格条件下,建立了拟近似解的最优性充要条件.其次给出了鲁棒凸优化问题拟近似解在Wolf型和Mond-weir型对偶模型下的强(弱)对偶定理.最后给出具体实例验证了本文获得的结果.     

多目标优化问题McRow最优解的刻画

基于多目标优化问题的McRow模型,该文确定了W?鲁棒有效解(也称为McRow最优解)与弱有效解、有效解以及真有效解的关系.首先,针对确定多目标优化问题,研究了W?鲁棒有效解与各种精确解的关系.随后,针对随机多目标优化问题,引进McRow最优解的概念,给出了它与其余各种解的关系.算例表明,利用McRow模型所得到的解更...     

非光滑多目标优化问题的最优性条件

本文利用极值原理在Fréchet次微分下研究了非光滑多目标优化问题的最优性条件.首先,研究了非光滑半无限多目标优化问题的必要性条件.随后,建立了非光滑多目标优化问题Henig真有效解的必要条件.     

不确定信息下分式半无限优化问题的近似最优性刻画

该文研究了一类带不确定参数的多目标分式半无限优化问题.首先借助鲁棒优化方法,引入该不确定多目标分式优化问题的鲁棒对应优化模型,并借助Dinkelbach方法,将该鲁棒对应优化模型转化为一般的多目标优化问题.随后借助一种标量化方法,建立了该优化问题的标量化问题,并刻画了它们的解之间的关系.最后借助一类鲁棒型次微分约束规格,建立了该不确定多目标分式优化问题拟近似有效解的鲁棒最优性条件.     

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...     

集优化问题的近似Benson真有效解及非线性刻画

利用集合的Minkowski差,引进集优化问题的Benson真有效解和近似Benson真有效解的概念,讨论了它们之间的关系.在某种假设下证明了近似Benson真有效解集是闭的.利用非线性泛函分别建立了无约束和带约束集优化问题取得近似Benson真有效解的必要条件.     

广义凸函数及非光滑多目标规划真有效解的充分条件

本文给出了一类广义凸函数的统一定义，在锥意义下，得出了非光滑多目标规划真有效解的充分条件，推广了以往的结论．     

有限理性与多目标问题解的稳定性

文章对多目标最优化问题定义了理性函数,证明了大多数的最优化问题(在Baire分类意义上)都是结构稳定的,对ε-平衡也都是鲁棒的.     

E-Borwein真有效解的刻画

基于Borwein真有效解的思想,利用free disposal集提出了向量优化问题的一类近似Borwein真有效解概念,建立了其与E-Benson真有效解间的等价关系     

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.     

Stackelberg Solutions to Multiobjective Two-Level Linear Programming Problems

In this paper, we consider a multiobjective two-level linear programming problem in which the decision maker at each level has multiple-objective functions conflicting with each other. The decision maker at the upper level must take account of multiple or infinite rational responses of the decision maker at the lower level in the problem. We examine three kinds of situations based on anticipation of the decision maker at the upper level: optimistic anticipation, pessimistic anticipation, and anticipation arising from the past behavior of the decision maker at the lower level. Mathematical programming problems for obtaining the Stackelberg solutions based on the three kinds of anticipation are formulated and algorithms for solving the problems are presented. Illustrative numerical examples are provided to understand the geometrical properties of the solutions and demonstrate the feasibility of the proposed methods.     

集值优化问题Borwein真有效解与Benson真有效解的等价性

在局部凸空间中锥弱似凸集值映射的假设下,集值优化问题Borwein真有效解与Benson真有效解的等价性被获得.为了说明结果,一些例子被给出.     

Nonsmooth Semi-infinite Multiobjective Optimization Problems

We apply some advanced tools of variational analysis and generalized differentiation to establish necessary conditions for (weakly) efficient solutions of a nonsmooth semi-infinite multiobjective optimization problem (SIMOP for brevity). Sufficient conditions for (weakly) efficient solutions of a SIMOP are also provided by means of introducing the concepts of (strictly) generalized convex functions defined in terms of the limiting subdifferential of locally Lipschitz functions. In addition, we propose types of Wolfe and Mond–Weir dual problems for SIMOPs, and explore weak and strong duality relations under assumptions of (strictly) generalized convexity. Examples are also designed to analyze and illustrate the obtained results.     

向量优化问题有效解的稳定性

运用标量化的方法,通过锥正定真有效解的上半连续性讨论了无限维赋范空间中锥有效解的部分上半连续性,证明了锥有效解的通有稳定性.在此基础上,进一步证明,在Baire纲的意义下,绝大多数的向量优化问题至少存在一个锥正定真有效解是本质的有效解,换句话说,绝大多数的向量优化问题锥有效解是几乎下半连续的.