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Journal of Systems Science & Complexity 2014年第2期27卷 276-288页

作者： SUN Yudong SHI Yimin GU Xin Department of Applied Mathematics Northwestern Polytechnical University Department of Methodology and Statistics Utrecht University

This paper studies the nonlinear variational inequality.with integro-differential term arising from valuation of American style double barrier option. First, the authors use the penalty method to transform the variational inequality.into a nonlinear parabolic initial boundary problem(i.e., penalty problem). Second, the existence and uniqueness of solution to the penalty problem are proved by using the Scheafer fixed point theory. Third, the authors prove the existence of variational inequality. solution by showing the fact that the penalized PDE converges to the variational inequality. The uniqueness of solution to the variational inequality.is also proved by contradiction.

关键词： American style barrier option existence integro-differential uniqueness variational inequality.

A GENERAL ITERATIVE METHOD OF FIXED POINTS FOR EQUILIBRIUM PROBLEMS AND OPTIMIZATION PROBLEMS

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Journal of Systems Science & Complexity 2009年第3期22卷 503-517页

作者： Fang ZHANG·Yongfu SUDepartment of Mathematics,Tianjin Polytechnic University,Tianjin 300160,China. Department of Mathematics Tianjin Polytechnic University

The purpose of this paper is to present a general iterative scheme as below：{F（un,y）＋1/rn（y-un,un-xn）≥0,y∈C,xn＋1=（I-αnA）Sun＋αnγf（xn）and to prove that, if {an} and {rn} satisfy appropriate conditions, then iteration sequences {xn} and {un} converge strongly to a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solution of a variational inequality. too. Furthermore, by using the above result, we can also obtain an iterative algorithm for solution of an optimization problem min h（x）, where h（x） is a convex and lower semicontinuous functional defined on a closed convex subset C of a Hilbert space H. The results presented in this paper extend, generalize and improve the results of Combettes and Hirstoaga, Wittmann, ***, Giuseppe Marino, Hong-Kun Xu, and some others.

关键词： Eprilibriurn problem nonexpansive mappings optimization problem strong convergence variational inequality.

THREE-STEP ITERATIONS FOR NONEXPANSIVE MAPPINGS AND INVERSE-STRONGLY MONOTONE MAPPINGS

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Journal of Systems Science & Complexity 2009年第2期22卷 333-344页

作者： Meijuan SHANG Yongfu SU Xiaolong QIN Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Department of Mathematics Shijiazhuang University Shijiazhuang 050035 China Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China. Department of Mathematics and the Research Institute of Natural Sciences Gyeongsang National UniversityChinju 660-701 Korea.

This paper introduces a three-step iteration for finding a common element of the set of fixedpoints of a nonexpansive mapping and the set of solutions of the variational inequality.for an inverse-strongly monotone mapping by viscosity approximation methods in a Hilbert *** authors showthat the iterative sequence converges strongly to a common element of the two sets,which solves somevariational ***,the authors consider the problem of finding a common fixed pointof a nonexpansive mapping and a strictly pseudo-contractive mapping and the problem of finding acommon element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse-strongly monotone *** results obtained in this paper extend and improve the correspondingresults announced by Nakajo,Takahashi,and Toyoda.

关键词： Inverse-strongly monotone mapping metric projection nonexpansive mapping variational inequality.

A minimax inequality.and variational inequalities

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Progress in Natural Science:Materials International 1997年第1期 94-101页

作者：程曹宗 Beijing 100044 Beijing Polytechnic University China Computer Institute

A generalization of the Ky Fan’s lemma is obtained. By this generalization a minimax inequality.oftwo functions on X × Y with topological vector spaces X and Y is proved. This inequality.extends some results due to ... 详细信息

关键词： topological vector space nonlinear function minimax inequality variational inequality.

一种基于增广拉格朗日的并行分裂方法求解网络资源分配问题

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高等学校计算数学学报 2014年第4期36卷 345-359页

作者：王群蔡邢菊何洪津南京师范大学数学科学学院杭州电子科技大学理学院

1问题描述网络资源分配问题是一类约束优化问题,网络具有一个有限容量的资源并且用户的数量是有限的.当用户需要争夺资源,就需要一个控制机制来分配资源,避免网络拥塞.实际中,需要尽量保证网络中的每个用户应该能够充分利用有限的资源,... 详细信息

1问题描述网络资源分配问题是一类约束优化问题,网络具有一个有限容量的资源并且用户的数量是有限的.当用户需要争夺资源,就需要一个控制机制来分配资源,避免网络拥塞.实际中,需要尽量保证网络中的每个用户应该能够充分利用有限的资源,并且不会对网络中其他用户造成不必要干扰,同时得到高的满意度.因此,每个用户的效用是通过一个与分配给用户资源有关的函数来定义,每个用户的效用函数也可以被建模为分配给所有用户

关键词： splitting method network resource allocation problem variational inequality.

Regularity of obstacle optimal control problem

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Journal of Shanghai University(English Edition) 2006年第1期10卷 1-3页

作者：郭兴明李秀华 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072 P.R.China

In this paper, by investigating an optimal control problem which is equivalent to original problem, the regularity of an obstacle optimal control problem was treated. Furthermore, based on some properties of operator ... 详细信息

关键词： regularity obstacle problem variational inequality.