共查询到20条相似文献,搜索用时 15 毫秒
1.
Tomonari Suzuki 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2204-2209
It is well known that the famous Ekeland variational principle characterizes the metric completeness of underlying spaces. In this paper, we prove that some versions of the strong Ekeland variational principle characterize the reflexivity and the compactness of underlying spaces. 相似文献
2.
Through a simple extension of Brézis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion. 相似文献
3.
Proper Efficiency in Locally Convex Topological Vector Spaces 总被引:18,自引:0,他引:18
We present a general treatment of proper efficiency, which was originally given in normed vector spaces; we introduce a new kind of efficiency in locally convex topological vector spaces. We examine the relationships among these efficiencies. As an application, we prove a strong Ekeland variational principle. 相似文献
4.
Leszek Gasiński 《Journal of Global Optimization》2007,38(3):459-478
In this paper, we study the existence of multiple solutions for nonlinear scalar periodic problems at resonance with p-Laplacian-like operator. Using the Ekeland variational principle a two-solution theorem is obtained and using also a local
linking theorem a three-solution theorem is proved.
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5.
J. H. Chabrowski 《Ricerche di matematica》2011,60(2):333-350
In this note we consider a class of semilinear elliptic variational inequalities on H
1(Ω) space. With the aid of the mountain-pass principle and the Ekeland variational principle we prove the existence of solutions. 相似文献
6.
As shown by F. Sullivan (Proc. Am. Math. Soc. 83:345–346, 1981), validity of the weak Ekeland variational principle implies completeness of the underlying metric space. In this note, we
show that what really forces completeness in Sullivan’s argument is an even simpler geometric property of lower bounded Lipschitz
functions. We derive the weak Ekeland principle from this new property, and use the new property to directly obtain an omnibus
non-empty intersection result for decreasing sequences of closed sets that yields as special cases the theorems of Cantor
and Kuratowski valid in complete metric spaces 相似文献
7.
有界线性空间中引入了Q-距离的概念,建立了一类向量值Ekeland变分原理,其目标函数是从有界线性空间映到锥序的实线性空间,并且扰动项中含有Q-距离.由此可以得到有界线性空间中现有的一些Ekeland变分原理.同时建立了有界线性空间中的向量值Caristi不动点定理,也给出二者的等价性. 相似文献
8.
We establish a pre-order principle. From the principle, we obtain a very general set-valued Ekeland variational principle, where the objective function is a set-valued map taking values in a quasi-ordered linear space and the perturbation contains a family of set-valued maps satisfying certain property. From this general set-valued Ekeland variational principle, we deduce a number of particular versions of set-valued Ekeland variational principle, which include many known Ekeland variational principles, their improvements and some new results. 相似文献
9.
Ekeland变分原理在最优化理论及应用研究中具有十分重要的作用.利用非线性标量化函数及相应的非凸分离定理建立了基于改进集的集值Ekeland变分原理.新的Ekeland变分原理包含了一些经典的Ekeland变分原理作为其特例. 相似文献
10.
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
11.
We use the basic formulation of Ekeland’s variational principle to establish characterizations of complete path metric spaces
which, being described in terms of the strong slope, are called coherent as in [3]. We also provide some basic nonlinear error bound and metric regularity results, in the context of coherent spaces. 相似文献
12.
Marc Lassonde 《Set-Valued and Variational Analysis》2009,17(2):183-193
Given a pair of Banach spaces X and Y such that one is the dual of the other, we study the relationships between generic Fréchet differentiability of convex continuous
functions on Y (Asplund property), generic existence of linear perturbations for lower semicontinuous functions on X to have a strong minimum (Stegall variational principle), and dentability of bounded subsets of X (Radon-Nikodym Property).
相似文献
13.
A revised pre-order principle and set-valued Ekeland variational principles with generalized distances 下载免费PDF全文
Jing Hui Qiu 《数学学报(英文版)》2017,33(6):775-792
In my former paper "A pre-order principle and set-valued Ekeland variational principle"(see [J. Math. Anal. Appl., 419, 904–937(2014)]), we established a general pre-order principle.From the pre-order principle, we deduced most of the known set-valued Ekeland variational principles(denoted by EVPs) in set containing forms and their improvements. But the pre-order principle could not imply Khanh and Quy's EVP in [On generalized Ekeland's variational principle and equivalent formulations for set-valued mappings, J. Glob. Optim., 49, 381–396(2011)], where the perturbation contains a weak τ-function, a certain type of generalized distances. In this paper, we give a revised version of the pre-order principle. This revised version not only implies the original pre-order principle,but also can be applied to obtain the above Khanh and Quy's EVP. In particular, we give several new set-valued EVPs, where the perturbations contain convex subsets of the ordering cone and various types of generalized distances. 相似文献
14.
Jian-Wen Peng 《Journal of Global Optimization》2007,39(3):441-457
In this paper, we introduce and study a new system of variational inclusions with (A, η, m)-accretive operators which contains variational inequalities, variational inclusions, systems of variational inequalities
and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (A, η, m)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multi-step iterative
algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unifies, extends and improves some known results in the literature.
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15.
In this note, we present a generalization of the celebrated Ekeland variational principle and its equivalent forms. The results presented in this paper unify, improve, and extend the corresponding result in Refs. 1–7. 相似文献
16.
Yousuke Araya 《Applied Mathematics Letters》2009,22(4):501-504
We present a simple proof of vectorial Takahashi’s nonconvex minimization theorem based on Gopfert, Tammer and Zalinescu [A. Gopfert, C. Tammer, C. Zalinescu, On the vectorial Ekeland’s variational principle and minimal points in product spaces, Nonlinear Anal. 39 (2000) 909–922; C. Tammer, A variational principle and a fixed point theorem, in: System Modelling and Optimization (Compiegne, 1993), in: Lecture Notes in Control and Inform. Sci., vol. 197, Springer, London, 1994, pp. 248–257]. 相似文献
17.
In this paper,we study error bounds for lower semicontinuous functions defned on Banach space and linear regularity for fnitely many closed subset in Banach spaces.By using Clarke's subdiferentials and Ekeland variational principle,we establish several sufcient conditions ensuring error bounds and linear regularity in Banach spaces. 相似文献
18.
K.R. Kazmi B.S. Komal F.A. Khan Pankaj Mansotra 《Applied mathematics and computation》2009,215(2):716-726
In this paper, using the concept of P-η-proximal-point mapping introduced by Kazmi and Bhat [11], we study the existence and sensitivity analysis of the solution set of a system of parametric general quasi-variational-like inequality problems in uniformly smooth Banach spaces. Further under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameters. The approach used in this paper may be treated as an extension and unification of approaches for studying sensitivity analysis for various important classes of variational inequalities given in [1,2,4,12,14–16,21–24]. 相似文献
19.
In this paper, we study error bounds for lower semicontinuous functions defined on Banach space and linear regularity for finitely many closed subset in Banach spaces. By using Clarke's subd- ifferentials and Ekeland variational principle, we establish several sufficient conditions ensuring error bounds and linear regularity in Banach spaces. 相似文献
20.
Let X and Y be Hausdorff topological vector spaces, K a nonempty, closed, and convex subset of X, C : K → 2Y a point-to-set mapping such that for any χ ε K, C(χ) is a pointed, closed, and convex cone in Y and int C(χ) ≠ 0. Given a mapping g : K → K and a vector valued bifunction f : K × K → Y, we consider the implicit vector equilibrium problem (IVEP) of finding χ* ε K such that f g(χ*), y) -int C(χ) for all y ε K. This problem generalizes the (scalar) implicit equilibrium problem and implicit variational inequality problem. We propose the dual of the implicit vector equilibrium problem (DIVEP) and establish the equivalence between (IVEP) and (DIVEP) under certain assumptions. Also, we give characterizations of the set of solutions for (IVP) in case of nonmonotonicity, weak C-pseudomonotonicity, C-pseudomonotonicity, and strict C-pseudomonotonicity, respectively. Under these assumptions, we conclude that the sets of solutions are nonempty, closed, and convex. Finally, we give some applications of (IVEP) to vector variational inequality problems and vector optimization problems. 相似文献