共查询到20条相似文献,搜索用时 15 毫秒
1.
Le Anh Tuan 《Numerical Functional Analysis & Optimization》2013,34(1):78-95
In this paper, I introduce two kinds of ε-subgradients—ε-Pareto subgradients and ε-Benson proper subgradients—for set-valued maps. I give sufficient conditions for the existence of such ε-subgradients. A generalized ε-Moreau–Rockafellar type theorem for ε-Benson proper subdifferentials of set-valued maps is formulated and applied to establish ε-optimality conditions for ε-Benson proper efficient solutions of vector optimization problems with set-valued maps. Scalarization theorems for such a problem are also obtained. 相似文献
2.
K. R. Kazmi 《Journal of Optimization Theory and Applications》2001,109(3):667-674
The -generalized minima for vector optimization problems are defined and a sufficient condition for the existence of -generalized minima for vector optimization problems is established. 相似文献
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In this paper,the ε-super effcient solution for set-valued map vector optimization in locally convex space is introduced.And under the assumption of the nearly generalized cone-subconvexlikeness for set-valued maps,used new methods,the scalarization theorem and Lagrange multiplier theorem for ε-super effcient solution are established. 相似文献
5.
Existence of Solutions to Generalized Vector Quasi-Equilibrium Problems with Discontinuous Mappings 总被引:2,自引:0,他引:2
Ya Ping FANG Nan Jing HUANG 《数学学报(英文版)》2006,22(4):1127-1132
Let X, Y be two finite-dimensional topological vector spaces, Z a Hausdorff topological vector space, K C X and D C Z be two nonempty sets, C be a pointed, closed, and convex cone in Y with int C ≠θ Let S : K → 2^K and T : K → 2^D be two multivalued mappings, and φ : K × D × K → Y be a trifunction. In this paper, we consider the generalized vector quasi-equilibrium problem, which is formulated by finding X∈ K and y∈ T(x) such that x∈ E S(x) and φ(x,y, u) (∈/) -int C for all u ∈ S(x). We establish an existence result in which T is not supposed to have any continuity property. Our results extend and improve the corresponding results of Cubiotti, Yao and Guo. 相似文献
6.
This paper deals with the generalized Clarke epiderivative of the extremum (or efficient point) multifunction in parametric
vector optimization problems. The formulas for computing and/or estimating the generalized Clarke epiderivative of this extremum
multifunction are given in terms of the Clarke tangent cone to the graph of a multifunction or the constraint mapping and/or
the Fréchet derivative of the objective function. An application to semi-infinite programming is given. 相似文献
7.
In this article, using the nonlinear scalarization approach by virtue of the nonlinear scalarization function, commonly known as the Gerstewitz function in the theory of vector optimization, Hölder continuity of solution mappings for both set-valued and single-valued cases to parametric vector equilibrium problems is studied. The nonlinear scalarization function is a powerful tool that plays a key role in the proofs, and its main properties (such as sublinearity, continuity, convexity) are fully employed. Especially, its locally and globally Lipschitz properties are provided and the Lipschitz property is first exploited to investigate the Hölder continuity of solutions. 相似文献
8.
JINDE WANG 《运筹学学报》1998,(1)
1.IntroductionDistributionproblemsareofgreatimportanceinstochasticoptimizationandstatis-tics.Usuallythiskindofproblemscanbedescribedinthefollowingform:wheref(x,w)isafuncti0ndefinedonR"xflandSisasubsetin'R".Because0fc0mplexityoftheproblems,ingeneral,onecangetonlytheirapproximatesolutions.Thefollowingtypeofapproximationis0ftenused:Letuscall(2)thefirsttype0fapproximation.DenotebyZ(w),A(w)theoptima1valueandoptimalsolutionsetofproblem(1)respectivelyandbyZk(w),Ak(w)thecorrespondingonesofproblem(… 相似文献
9.
The vector optimization problem may have a nonsmooth objective function. Therefore, we introduce the Minty vector variational
inequality (Minty VVI) and the Stampacchia vector variational inequality (Stampacchia VVI) defined by means of upper Dini
derivative. By using the Minty VVI, we provide a necessary and sufficient condition for a vector minimal point (v.m.p.) of
a vector optimization problem for pseudoconvex functions involving Dini derivatives. We establish the relationship between
the Minty VVI and the Stampacchia VVI under upper sign continuity. Some relationships among v.m.p., weak v.m.p., solutions
of the Stampacchia VVI and solutions of the Minty VVI are discussed. We present also an existence result for the solutions
of the weak Minty VVI and the weak Stampacchia VVI. 相似文献
10.
1.IntroductionTheoptimalityconditionsofmathematicalprogrammingisaveryimportantsubjectbecausetLeyprovideausefulanalyticaltoolforstudingthedualitytheoryandnonlinearprogrammingalgoirthms.Inrecelltyears,someauthorshavebeguntostudytheoptimalityconditionsforvectoroptimizationproblemofset-valuedmapping,suchas[4][51.Inthispaperlwedefinetheconceptofcone--weaklyefficientsubdifferentialofset-valuedmappinginthecaseofgeneralpartiallyorderedlocallyconvextopologicalvectorspaces.Thecone-weaklysubdifferential… 相似文献
11.
X. X. Huang 《Numerical Functional Analysis & Optimization》2013,34(4):440-459
The Levitin–Polyak well-posedness for a constrained problem guarantees that, for an approximating solution sequence, there is a subsequence which converges to a solution of the problem. In this article, we introduce several types of (generalized) Levitin–Polyak well-posednesses for a vector variational inequality problem with both abstract and functional constraints. Various criteria and characterizations for these types of well-posednesses are given. Relations among these types of well-posednesses are presented. 相似文献
12.
Hyungjin Huh 《偏微分方程通讯》2013,38(2):235-243
We study blow-up solutions of modified Schrödinger maps. We observe the pseudo-conformal invariance by which explicit blow-up solutions can be constructed. 相似文献
13.
The Existence of Solutions to Sturm-Liouville Boundary Value Problems with Laplacian-like Operator 总被引:2,自引:0,他引:2
Wei-ping Sun Wei-gao GeDepartment of Applied Mathematics Beijing Institute of Technology Beijing China 《应用数学学报(英文版)》2002,18(2):341-348
Abstract The existence of infinitely many solutions to Sturm-Liouville boundary value problem with aLaplacian-like operator is studied by applying generalized polar coordinates. 相似文献
14.
Henig Efficiency in Vector Optimization with Nearly Cone-subconvexlike Set-valued Functions 总被引:1,自引:0,他引:1
Qiu-sheng Qiu 《应用数学学报(英文版)》2007,23(2):319-328
In this paper,we study Henig efficiency in vector optimization with nearly cone-subconvexlikeset-valued function.The existence of Henig efficient point is proved and characterization of Henig efficiencyis established using the method of Lagrangian multiplier.As an interesting application of the results in thispaper,we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly cone-subconvexlike set-valued function. 相似文献
15.
《中学生数学》2007,(6)
Imaging that there is a part of the map of Sentosa Island.It reasonably represents the rela- tive positions of interest.The scale shown at the bottom centre of this map gives a measure of the ratio of the distance on the map to the actural distance. In this case,4 cm on the map represents 1 km.since a scale can be expressed in a ratio form, we have: 相似文献
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An-hua Wan Jun-yi Fu Wei-hua Mao 《应用数学学报(英文版)》2006,22(1):21-26
A new generalized vector equilibrium problem involving set-valued mappings and the proper quasi concavity of set-valued mappings in topological vector spaces are introduced; its existence theorems and the convexity of the solution sets are established. 相似文献
18.
Journal of Optimization Theory and Applications - In this paper, we study a general minimization vector problem which is expressed in terms of a perturbation mapping defined on a product of locally... 相似文献
19.
On Singular Solutions of Boundary Value Problems for Quasilinear Parabolic Equations with Absorption 总被引:1,自引:0,他引:1
The existence and nonexistence of non-trivial solutions for the boundary value problemare studied. 相似文献
20.
Xie Ping DING 《数学学报(英文版)》2006,22(5):1529-1538
A new class of locally finite continuous topological spaces (for short, locally FC-spaces) and a class of system of generalized vector quasi-equilibrium problems are introduced. By applying a generalized Himmelberg type fixed point theorem for a set-valued mapping with KKM-property due to the author, a collectively fixed point and an equilibrium existence theorem of generalized game are first proved in locally FC-spaces. By applying our equilibrium existence theorem of generalized game, some new existence theorems of equilibrium points for the system of generalized vector quasi-equilibrium problems are proved in locally FC-spaces. These theorems improve, unify and generalize many known results in the literatures. 相似文献