共查询到20条相似文献,搜索用时 15 毫秒
1.
利用标量化方法建立对称向量拟均衡问题有效解的存在性定理.作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理. 相似文献
2.
Xun-Hua Gong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3598-3612
In this paper, we investigated vector equilibrium problems and gave the scalarization results for weakly efficient solutions, Henig efficient solutions, and globally efficient solutions to the vector equilibrium problems without the convexity assumption. Using nonsmooth analysis and the scalarization results, we provided the necessary conditions for weakly efficient solutions, Henig efficient solutions, globally efficient solutions, and superefficient solutions to vector equilibrium problems. By the assumption of convexity, we gave sufficient conditions for those solutions. As applications, we gave the necessary and sufficient conditions for corresponding solutions to vector variational inequalities and vector optimization problems. 相似文献
3.
Refail Kasimbeyli 《Journal of Global Optimization》2013,56(2):279-297
This paper presents the conic scalarization method for scalarization of nonlinear multi-objective optimization problems. We introduce a special class of monotonically increasing sublinear scalarizing functions and show that the zero sublevel set of every function from this class is a convex closed and pointed cone which contains the negative ordering cone. We introduce the notion of a separable cone and show that two closed cones (one of them is separable) having only the vertex in common can be separated by a zero sublevel set of some function from this class. It is shown that the scalar optimization problem constructed by using these functions, enables to characterize the complete set of efficient and properly efficient solutions of multi-objective problems without convexity and boundedness conditions. By choosing a suitable scalarizing parameter set consisting of a weighting vector, an augmentation parameter, and a reference point, decision maker may guarantee a most preferred efficient or properly efficient solution. 相似文献
4.
Efficiency and Henig Efficiency for Vector Equilibrium Problems 总被引:6,自引:0,他引:6
We introduce the concept of Henig efficiency for vector equilibrium problems, and extend scalarization results from vector optimization problems to vector equilibrium problems. Using these scalarization results, we discuss the existence of the efficient solutions and the connectedness of the set of Henig efficient solutions to the vector-valued Hartman–Stampacchia variational inequality. 相似文献
5.
Adela Capătă 《Journal of Global Optimization》2011,51(4):657-675
In this paper, we present sufficient conditions for the existence of Henig efficient solutions, superefficient solutions and
Henig globally efficient solutions of a vector equilibrium problem in topological vector spaces, using a well-known separation
theorem in infinite dimensional spaces. As an application, using a scalarization technique, existence results for proper efficient
solutions of generalized vector variational inequalities are given. 相似文献
6.
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. 相似文献
7.
A Nonlinear Scalarization Function and Generalized Quasi-vector Equilibrium Problems 总被引:1,自引:0,他引:1
Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization
problems can be found by solving scalar optimization problems. In this paper we introduce a nonlinear scalarization function
for a variable domination structure. Several important properties, such as subadditiveness and continuity, of this nonlinear
scalarization function are established. This nonlinear scalarization function is applied to study the existence of solutions
for generalized quasi-vector equilibrium problems.
This paper is dedicated to Professor Franco Giannessi for his 68th birthday 相似文献
8.
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. 相似文献
9.
Bui Trong Kien Ngai Ching Wong Jen-Chih Yao 《Nonlinear Analysis: Theory, Methods & Applications》2008
It is well known that a vector variational inequality can be a very efficient model for use in studying vector optimization problems. By using the Ky Fan fixed point theorem and the scalarization method we will prove some existence theorems for strong solutions for generalized vector variational inequalities where discontinuous and star-pseudomonotone operators are involved. Our results can be applied to the study of the existence of solutions of vector optimal problems. Some examples are given and analyzed. 相似文献
10.
We study the weak domination property and weakly efficient solutions in vector optimization problems. In particular scalarization
of these problems is obtained by virtue of some suitable merit functions. Some natural conditions to ensure the existence
of error bounds for merit functions are also given.
This research was supported by a direct grant (CUHK) and an Earmarked Grant from the Research Grant Council of Hong Kong. 相似文献
11.
12.
Under the assumption that the ordering cone has a nonempty interior and is separable (or the feasible set has a nonempty interior and is separable), we give scalarization theorems on Benson proper effciency. Applying the results to vector optimization problems with nearly cone-subconvexlike set-valued maps, we obtain scalarization theorems and Lagrange multiplier theorems for Benson proper effcient solutions. 相似文献
13.
Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings
In this paper, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued
mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three
examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite
dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore,
a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.
相似文献
14.
We consider vector optimization problems on Banach spaces without convexity assumptions. Under the assumption that the objective function is locally Lipschitz we derive Lagrangian necessary conditions on the basis of Mordukhovich subdifferential and the approximate subdifferential by Ioffe using a non-convex scalarization scheme. Finally, we apply the results for deriving necessary conditions for weakly efficient solutions of non-convex location problems. 相似文献
15.
In a recent paper by Li (Ref. 1), a scheme was proposed to convexify an efficient frontier for a vector optimization problem by rescaling each component of the vector objective functions by its p-power. For sufficiently large p, it was shown that the transformed efficient frontier is cone-convex; hence, the usual linear scalarization (or supporting hyperplane) method can be used to find the efficient solutions. An outstanding question remains: What is the minimum value of p such that the efficient frontier can be convexified? In this note, we answer the above question by deriving some theoretical lower bounds for p.
相似文献16.
In this paper, two existence theorems concerning the strong efficient solutions and the weakly efficient solutions of generalized vector equilibrium problems are derived by using the Fan-KKM Theorem and an existence theorem for the efficient solutions of generalized vector equilibrium problems is established by using the scalarization method. Moreover, the lower semicontinuity of the strong efficient solution mapping and the weakly efficient solution mapping to parametric generalized vector equilibrium problems are showed under suitable conditions with neither monotonicity nor any information of the solution mappings. Finally, some applications to the vector optimization problems and the Stackelberg equilibrium problem are also given. 相似文献
17.
Connectedness of the Solution Sets and Scalarization for Vector Equilibrium Problems 总被引:3,自引:0,他引:3
X. H. Gong 《Journal of Optimization Theory and Applications》2007,133(2):151-161
In this paper, we introduce the concepts of globally efficient solution and cone-Benson efficient solution for a vector equilibrium
problem; we give some scalarization results for Henig efficient solution sets, globally efficient solution sets, weak efficient
solution sets, and cone-Benson efficient solution sets in locally convex spaces. Using the scalarization results, we show
the connectedness and path connectedness of weak efficient solution sets and various proper efficient solution sets of vector
equilibrium problem.
This research was partially supported by the National Natural Science Foundation of China and the Natural Science Foundation
of Jinxing Province, China. 相似文献
18.
Nguyen Van Hung Vo Minh Tam Dumitru Baleanu 《Mathematical Methods in the Applied Sciences》2020,43(7):4614-4626
In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new. 相似文献
19.
In this paper we focus on minimal points in linear spaces and minimal solutions of vector optimization problems, where the preference relation is defined via an improvement set E. To be precise, we extend the notion of E-optimal point due to Chicco et al. in [4] to a general (non-necessarily Pareto) quasi ordered linear space and we study its properties. In particular, we relate the notion of improvement set with other similar concepts of the literature and we characterize it by means of sublevel sets of scalar functions. Moreover, we obtain necessary and sufficient conditions for E-optimal solutions of vector optimization problems through scalarization processes by assuming convexity assumptions and also in the general (nonconvex) case. By applying the obtained results to certain improvement sets we generalize well-known results of the literature referred to efficient, weak efficient and approximate efficient solutions of vector optimization problems. 相似文献
20.
In this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient
solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of
the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium
problem are proved in locally convex spaces. 相似文献