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ON THE GENERALIZED FRITZ JOHN OPTIMALITY CONDITIONS OF VECTOR OPTIMIZATION WITH SET-VALUED MAPS UNDER BENSON PROPER EFFICIENCY 被引量:3
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作者 盛宝怀 刘三阳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第12期1444-1451,共8页
A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condit... A kind of tangent derivative and the concepts of strong and weak * pseudoconvexity for a set-valued map are introduced. By the standard separation theorems of the convex sets and cones the optimality Fritz John condition of set-valued optimization under Benson proper efficiency is established, its sufficience is discussed. The form of the optimality conditions obtained here completely tally with the classical results when the set-valued map is specialized to be a single-valued map. 展开更多
关键词 contingent tangent cone set-valued map Benson proper efficiency Fritz John condition
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Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces 被引量:2
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作者 周志昂 《Journal of Shanghai University(English Edition)》 CAS 2010年第5期374-379,共6页
Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. U... Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency. 展开更多
关键词 set-valued maps vector closure generalized subconvexlikeness Benson proper efficient solution
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ε-super Effcient Solutions of Optimization Problems with Set-valued Maps in Locally Convex Space 被引量:1
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作者 WANG Shu-yu LIU Wan-li 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期26-31,共6页
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,u... 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. 展开更多
关键词 nearly generalized cone-subconvexlikeness set-valued map ε-super effcient solution lagrange multiplier
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Common Fixed Point Theorems for Sequences of φ-type Contraction Set-valued Mappings 被引量:9
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作者 WU Jian-rong LIU Hai-yan 《Chinese Quarterly Journal of Mathematics》 CSCD 2009年第4期504-510,共7页
In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a... In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained. 展开更多
关键词 sequence of set-valued mappings common fixed point random fixed point metric space
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Formal Concept Analysis Based on Set-valued Mapping
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作者 CHEN Li-ya HUANG Tao +1 位作者 SONG Zhen-ming PEI Zheng 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期390-396,共7页
Formal concept analysis (FCA) is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, e... Formal concept analysis (FCA) is a discipline that studied the hierarchical structures induced by a binary relation between a pair of sets, and applies in data analysis, information retrieval, knowledge discovery, etc. In this paper, it is shown that a formal context T is equivalent to a set-valued mapping S : G → P(М), and formal concepts could be defined in the set-valued mapping S. It is known that the topology and set-valued mapping are linked. Hence, the advantage of this paper is that the conclusion make us to construct formal concept lattice based on the topology. 展开更多
关键词 FCA set-valued mapping ISOMORPHISM
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Natural Mappings on Set-valued Mapping Spaces
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作者 LI Zu-quan WANG Jiu-jing 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期21-25,共5页
In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued ... In this paper,we discuss the continuities of some natural mappings on pointcompact continuous set-valued mapping spaces with compact-open topology and obtain the properties of set-valued injective mappings,set-valued diagonal mappings,induced mappings,set-valued evaluation mappings,set-valued topological sum mappings and set-valued topological product mappings. 展开更多
关键词 set-valued mapping compact-open topology natural mapping
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Proximal point algorithm for a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings
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作者 李红刚 《Journal of Chongqing University》 CAS 2008年第1期79-84,共6页
We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approx... We introduced a new class of fuzzy set-valued variational inclusions with (H,η)-monotone mappings. Using the resolvent operator method in Hilbert spaces, we suggested a new proximal point algorithm for finding approximate solutions, which strongly converge to the exact solution of a fuzzy set-valued variational inclusion with (H,η)-monotone. The results improved and generalized the general quasi-variational inclusions with fuzzy set-valued mappings proposed by Jin and Tian Jin MM, Perturbed proximal point algorithm for general quasi-variational inclusions with fuzzy set-valued mappings, OR Transactions, 2005, 9(3): 31-38, (In Chinese); Tian YX, Generalized nonlinear implicit quasi-variational inclusions with fuzzy mappings, Computers & Mathematics with Applications, 2001, 42: 101-108. 展开更多
关键词 variational inclusion (H η)-monotone mapping resolvent operator technique fuzzy set-valued mapping proximal point algorithm: convergence of numerical methods
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Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces
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作者 张勇 《Journal of Southwest Jiaotong University(English Edition)》 2006年第2期194-199,共6页
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in... A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results. 展开更多
关键词 Generalized set-valued Ф-hemi-contractive mapping Ishikawa and Mann iterative processes with errors q-uniformlysmooth Banach space Hausdorff metric Generalized duality mapping
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Iterative Approximation with Errors for Generalized Set-Valued Strongly Accretive Mapping in Banach Spaces
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作者 张勇 《Journal of Southwest Jiaotong University(English Edition)》 2007年第1期70-74,共5页
A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et ... A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al. 展开更多
关键词 Generalized set-valued strongly accretive mappings Ishikawa and Mann iterative processes with errors q-Uniformly Smooth Banach spaces Generalized duality mapping
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A survey of ergodicity on the set-valued mappings
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作者 ZHANGYu-cheng LIAOGong-fu 《海南师范学院学报(自然科学版)》 2004年第4期305-311,共7页
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
关键词 set-valued mapping INVARIANT measure ERGODIC MARKOV operator Mark-ov transition function lower SEMICONTINUOUS continuous selection
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THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION 被引量:2
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作者 盛保怀 刘三阳 《Acta Mathematica Scientia》 SCIE CSCD 2002年第1期47-55,共9页
The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz Joh... The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient. 展开更多
关键词 set-valued derivative optimality condition pseudoconvex set-valued mapping
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CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES 被引量:3
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作者 TIAN You-xian(田有先) +1 位作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1001-1008,共8页
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r... Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces. 展开更多
关键词 convex metric space fixed point generalized Ishikawa (Mann) iterative sequence with errors general quasi-contractive mapping
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Auxiliary principle and three-step iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities 被引量:1
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作者 徐海丽 郭兴明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第6期721-729,共9页
An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for... An auxiliary principle technique to study a class of generalized set-valued strongly nonlinear mixed variational-like inequalities is extended. The existence and uniqueness of the solution of the auxiliary problem for the generalized set-valued strongly nonlinear mixed variational-like inequalities are proved, a novel and innovative three-step iterative algorithm to compute approximate solution is constructed, and the existence of the solution of the generalized set-valued strongly nonlinear mixed variational-like inequality is shown using the auxiliary principle iterative sequences generated by the algorithm technique. The convergence of three-step is also proved. 展开更多
关键词 mixed variational-like inequality three-step iterative algorithm set-valued mapping auxiliary principle technique
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Existence and Algorithm of Solutions for Generalized Set-valued Strongly Nonlinear Mixed Variational-like Type Inequalities
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作者 胡梦瑜 曾六川 陈珊敏 《Journal of Donghua University(English Edition)》 EI CAS 2007年第4期467-472,477,共7页
The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for t... The auxiliary principle technique is extended to study a class of generalized set-valued strongly nonlinear mixed variational-like type inequalities. Firstly, the existence of solutions to the auxiliary problems for this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is shown. Secondly, the iterative algorithm for solving this class of generalized set-valued strongly nonlinear mixed variational-like type inequalities is given by using this existence result. Finally, the strong convergence of iterative sequences generated by the algorithm is proven. The present results improve, generalize and modify the earlier and recent ones obtained previously by some authors in the literature. 展开更多
关键词 iterative algorithm set-valued mapping EXISTENCE CONVERGENCE Hilbert space
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Projected subgradient method for non-Lipschitz set-valued mixed variational inequalities
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作者 唐国吉 黄南京 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第10期1345-1356,共12页
A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven tha... A projected subgradient method for solving a class of set-valued mixed variational inequalities (SMVIs) is proposed when the mapping is not necessarily Lipschitz. Under some suitable conditions, it can be proven that the sequence generated by the method can strongly converge to the unique solution to the problem in the Hilbert spaces. 展开更多
关键词 set-valued mixed Variational inequality (SMVI) projected subgradient method non-Lipschitz mapping CONVERGENCE
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Gap Functions and Error Bounds for Set-Valued Vector Quasi Variational Inequality Problems
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作者 Rachana Gupta Aparna Mehra 《Applied Mathematics》 2017年第12期1903-1917,共15页
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri... One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem. 展开更多
关键词 set-valued VECTOR QUASI Variational Inequality Problem GAP FUNCTION Regularized GAP FUNCTION Error Bounds Fixed Point Symmetric map α-Holder map
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Completely Generalized Strongly Set-valued Nonlinear Quasi-complementarity Problems
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作者 Dingpin Wu Zhi Ping Lui 《宜宾学院学报》 1998年第2期10-16,共7页
In this paper,we study a class of completely generalized strongly set-valued nonlinearquasi-complementarity problems and discuss the existence of solutions for this kind of quasi-complementariy problems without compac... In this paper,we study a class of completely generalized strongly set-valued nonlinearquasi-complementarity problems and discuss the existence of solutions for this kind of quasi-complementariy problems without compactness and the convergence of iterative sequencesgenerated by the algorithms. 展开更多
关键词 Quasi-complementarity problem set-valued mapPING algorithm.
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Sensitivity of the Product System of Set-Valued Non-Autonomous Discrete Dynamical Systems
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作者 Yongxi Jiang Tianxiu Lu +1 位作者 Jingmin Pi Xiaofang Yang 《Journal of Applied Mathematics and Physics》 2021年第11期2706-2716,共11页
This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" ... This paper is concerned with the sensitivity of set-valued discrete systems. Firstly, this paper obtained the equivalence between <img src="Edit_7024f70b-0568-4ca8-a554-c0d05abc0df0.bmp" alt="" />or <img src="Edit_95636a59-7d5d-4b6c-8bd5-f699dd9208df.bmp" alt="" /> and the product system <img src="Edit_c714caaf-0ed9-46bc-b3e1-b0223474a8f5.bmp" alt="" /> in sensitivity, infinite sensitivity, <em>F</em>-sensitivity, (<em>F</em><sub>1</sub>, <em>F</em><sub>2</sub>)-sensitivity. Then, the relation between (<em>X</em>, <em>f</em><sub>1,∞</sub>) or (<em>Y</em>, <em>g</em><sub>1,∞</sub>) and <img src="Edit_55b4ce47-89f3-4476-a8a8-4d4db5a4e8eb.bmp" alt="" /> in ergodic sensitivity is obtained. Where <img src="Edit_a99604c4-2f72-4e75-a998-8057b8790e03.bmp" alt="" /> is the set-valued dynamical system induced by a non-autonomous discrete dynamical system (<em>X</em>, <em>f</em><sub>1,∞</sub>). 展开更多
关键词 Sensitivity set-valued System Product mapping Non-Autonomous Systems
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Topological Stability and Entropy for Certain Set-valued Maps
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作者 Yu ZHANG Yu Jun ZHU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2024年第4期962-984,共23页
In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical sys... In this paper,the dynamics(including shadowing property,expansiveness,topological stability and entropy)of several types of upper semi-continuous set-valued maps are mainly considered from differentiable dynamical systems points of view.It is shown that(1)if f is a hyperbolic endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has theε-shadowing property,and moreover,if f is an expanding endomorphism then there exists a C^(1)-neighborhood U of f such that the induced set-valued map F_(f,U)has the Lipschitz shadowing property;(2)when a set-valued map F is generated by finite expanding endomorphisms,it has the shadowing property,and moreover,if the collection of the generators has no coincidence point then F is expansive and hence is topologically stable;(3)if f is an expanding endomorphism then for eachε>0 there exists a C^(1)-neighborhood U of f such that h(F_(f,U,ε))=h(f);(4)when F is generated by finite expanding endomorphisms with no coincidence point,the entropy formula of F is given.Furthermore,the dynamics of the set-valued maps based on discontinuous maps on the interval are also considered. 展开更多
关键词 set-valued map orbit space hyperbolic endomorphism perturbation SHADOWING EXPANSIVENESS topological stability ENTROPY
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Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epiderivative 被引量:2
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作者 Zhi-ang ZHOU Xin-min YANG Qiu-sheng QIU 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2018年第1期11-18,共8页
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epideriva... In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature. 展开更多
关键词 set-valued maps generalized cone convexity Henig proper efficiency contingent epiderivative optimality conditions
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