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1.
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
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强向量均衡问题与不动点问题的粘性逼近算法 总被引:2,自引:0,他引:2
讨论了强向量均衡问题与非扩张映射不动点问题的公共解.首先,给出了强向量均衡问题的辅助问题,并在适当的条件下,证明了其解的存在性和唯一性结果.然后,利用这些结果,提出了强向量均衡问题与非扩张映射不动点问题公共解的粘性逼近算法,并进一步证明了,在适当的条件下,由该算法产生的迭代序列强收敛于强向量均衡问题和非扩张映射不动点问题的公共解. 相似文献
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In this paper, we study the generalized vector equilibrium problems in real Hausdorff topological vector space settings. The concepts of weak solutions and strong solutions are introduced. Several new results of existence for the weak solutions and strong solutions of generalized vector equilibrium problems are derived. The new results extend and modify various existence theorems for similar problems. 相似文献
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Adela CAPĂTĂ 《数学物理学报(B辑英文版)》2017,37(2):463-476
The aim of this article is to present new existence results for globally efficient solutions of a strong vector equilibrium problem given by a sum of two functions via a generalized KKM principle, and to establish the connectedness of the solutions set. 相似文献
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广义投影下F隐变分不等式解的存在性 总被引:2,自引:0,他引:2
首先引进了广义(F,g)-投影算子,提出了一个新的例外簇概念,并运用Fan-KKM定理以及例外簇,分别在无单调性与渐近h-g伪单调假设下,研究了自反Banach空间中一类F隐变分不等式的可解性与解集特征问题,得到了新的解的存在性定理. 相似文献
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在拓扑向量空间中,利用Ky Fan截口定理得到一个锥凸向量拟均衡问题弱Pareto解的存在性结果.作为该结果的应用,得到了一个对称向量拟均衡问题在支付映射为锥凸条件下弱Pareto解的存在性定理.该定理在较弱的条件下回答了Fu在文献[1]中提出的第二个问题,即在支付映射为锥凸且连续的条件下对称向量拟均衡问题的弱Pareto解是否存在.最后在赋范线性空间中研究了锥凸对称向量拟均衡问题弱Pareto解集的通有稳定性. 相似文献
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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
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Ouayl Chadli Qamrul Hasan Ansari Suliman Al-Homidan 《Journal of Optimization Theory and Applications》2017,172(3):726-758
The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied. 相似文献
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Existence theorems for generalized vector variational inequalities with a variable ordering relation
In this paper we study the solvability of the generalized vector variational inequality problem, the GVVI problem, with a
variable ordering relation in reflexive Banach spaces. The existence results of strong solutions of GVVIs for monotone multifunctions
are established with the use of the KKM-Fan theorem. We also investigate the GVVI problems without monotonicity assumptions
and obtain the corresponding results of weak solutions by applying the Brouwer fixed point theorem. These results are also
the extension and improvement of some recent results in the literature. 相似文献
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Weak vector equilibrium problems with bi-variable mappings from product space of two bounded complete locally convex Hausdorff topological vector spaces to another topological vector space are studied. The existence theorems of solutions are proved by the FKKM fixed point theorem. Viscosity principle of vector equilibrium problems is dealt with. The relations between solutions of the vector equilibrium problem and those of its perturbation problem are presented. 相似文献
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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
13.
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
14.
提出一种具有控制结构的向量均衡问题与向量映射的新的伪单调性概念,得到具有控制结构的向量均衡问题解的存在性及其解集的紧凸性.作为应用,得到具有控制结构的向量变分不等式与互补问题的解. 相似文献
15.
主要研究平衡问题解的存在性.通过对目标函数和可行集合的渐近分析,给出拟单调平衡问题解集非空的条件.进而用类似的方法研究了向量平衡问题解存在的条件,并将其应用到向量优化问题上. 相似文献
16.
A linear stochastic continuity equation with non-regular coefficients is considered. We prove existence and uniqueness of strong solution, in the probabilistic sense, to the Cauchy problem when the vector field has low regularity, in which the classical DiPerna-Lions-Ambrosio theory of uniqueness of distributional solutions does not apply. We solve partially the open problem that is the case when the vector-field has random dependence. In addition, we prove a stability result for the solutions.
相似文献17.
Generalized Vector Equilibrium Problems with Trifunctions 总被引:4,自引:0,他引:4
In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given. 相似文献
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Y. C. Lin 《Journal of Optimization Theory and Applications》2009,142(3):557-568
In this paper, we study the F-implicit generalized (weak) case for vector variational inequalities in real topological vector spaces. Both weak and strong
solutions are considered. These two sets of solutions coincide whenever the mapping T is single-valued, but not set-valued. We use the Ferro minimax theorem to discuss the existence of strong solutions for F-implicit generalized vector variational inequalities. 相似文献
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In this paper, we study the existence of strong and weak solutions of the generalized vector equilibrium problems for trifunctions. Two special classes of vector-valued trifunctions are introdcued, called the classes of (SPM) and (GPM), respectively. Some existence results for strong solutions associated to functions of these classes are given. 相似文献