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具广义单调性的最优化问题与不动点问题的理论与算法
  • 项目名称：具广义单调性的最优化问题与不动点问题的理论与算法
  • 项目类别：面上项目
  • 批准号：10771141
  • 申请代码：A011201
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2009-12-31
  • 项目负责人：曾六川
  • 负责人职称：教授
  • 依托单位：上海师范大学
  • 批准年度：2007
中文摘要：

运用Banach空间几何学、线性拓扑空间理论、Banach空间中非线性逼近理论、不动点理论等现代分析的理论与方法，研究具广义单调性的最优化问题与不动点问题的理论与算法，即研究两个方面(1)具广义单调性的最优化问题解的存在性与迭代算法；(2)具广义单调性的算子不动点问题解的存在性与迭代算法．本项目将为迭代算法的研究提供新方法和新途径，并为现行数学技术提供强有力的工具，也为泛函空间中的算子逼近理论的研究和应用带来动力．本研究课题，是理论性和应用性都很强的边缘性交叉课题．在偏微分方程、力学、最优化与控制、运输与经济平衡、电路与结构分析，以及数学与工程科学中许多别的分支学科等方面都有着广泛应用．

中文主题词： 广义单调性；最优化问题；不动点问题；存在性；算法
结论摘要：

英文主题词generalized monotonicity; optimization problems; fixed-point problems; existence; algorithms

成果综合统计
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 73
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期刊论文
Strong convergence of iterative algorithms for variational inequalities in Banach spaces
Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous
On generalized variational-like inequalities with generalized monotone multivalued mappings
An iterative scheme for equilibrium problems and fixed point problems of strict pseudo-contraction m
New accuracy criteria for modified approximate proximal point algorithms in Hilbert spaces
Relaxed viscosity approximation methods for fixed point problems and variational inequality problems
An implicit iterative scheme for monotone variational inequalities and fixed point problems
Well-posedness of generalized mixed variational inequalities, inclusion problems and fixed-point pro
Hybrid proximal-point methods for common solutions of equilibrium problems and zeros of maximal mono
Viscosity approximation methods for equilibrium problems and fixed point problems of nonlinear semig
Necessary optimality conditions for super minimizers in structural problems of multiobjective optimi
On generalized implicit vector equilibrium problems in Banach spaces
Hybrid approximate proximal point algorithms for variational inequalities in Banach spaces ( J. Ineq
Hybrid viscosity-like approximation methods for nonexpansive mappings in Hilbert spaces
Modified extragradient methods for strict pseudo-contractions and monotone mappings
Viscosity approximation methods for strongly positive and monotone operators
Relaxed composite implicit iteration process for common fixed points of a finite family of strictly
On the characterization of strong convergence of an iterative algorithm for a class of multi-valued
On relaxed viscosity iterative methods for variational inequalities in Banach spaces
Two extragradient approximation methods for variational inequalities and fixed point problems of str
A hybrid extragradient method for general variational inequalities
Convergence of generalized projective modified iteration methods in Banach spaces
Viscosity approximation methods for generalized equilibrium problems and fixed point problems
Strong convergence of composite iterative schemes for zeros of $m$-accretive operators in Banach spa
Equivalence of generalized mixed complementarity and generalized mixed least element problems in ord
Existence of vector mixed variational inequalities in Banach spaces
Iterative Schemes for Generalized Equilibrium Problem and Two Maximal Monotone Operators (2009, Arti
Convergence analysis of iterative sequences for a pair of mappings in Banach spaces
Approximate proximal algorithms for generalized variational inequalities with pseudomonotone multifu
Hybrid viscosity approximation schemes for equilibrium problems and fixed point problems of infinite
Approximate proximal algorithms for generalized variational inequalities with paramonotonicity and p
A hybrid iterative scheme for mixed equilibrium problems and fixed point problems
On the convergence analysis of inexact hybrid extragradient proximal point algorithms for maximal mo
Iterative algorithm for finding approximate solutions of mixed quasi-variational-like inclusions
Iterative approximation of solutions for a class of completely generalized set-valued quasi-variatio
Existence of solutions for generalized vector variational-like inequalities
Fixed point solutions of variational inequalities for a finite family of asymptotically nonexpansive
General iterative algorithms for solving mixed quasi-variational-like inclusions 2455--2467.
Existence of solutions and variational principles for generalized vector systems
Well-posedness for mixed quasivariational-like inequalities
Generalized variational-like inequalities with compositely monotone-multifunctions
Approximation of common fixed points of families of nonexpansive mappings
Implicit iteration scheme with perturbed mapping for equilibrium problems and fixed point problems o
Existence theorems for generalized vector variational inequalities with pseudomonotonicity and their
On hybrid proximal-type algorithms in Banach spaces
On general variable-step relaxed projection method for strongly quasivariational inequalities
The viscosity approximation method for asymptotically nonexpansive mappings in Banach spaces
Generalized implicit hybrid projection-proximal point algorithm for maximal monotone operators in Hi
Strong convergence theorems by a relaxed extragradient method for a general system of variational in
Strong convergence of an iterative method with perturbed mappings for nonexpansive and accretive ope
A hybrid steepest-descent method for variational inequalities in Hilbert spaces
Mann-type steepest-descent and modified hybrid steepest-descent methods for variational inequalities
Strong weak convergence theorems of implicit hybrid steepest-descent methods for variational inequal
Weak convergence theorem by a modified extragradient method for nonexpansive mappings and monotone m
Mixed projection methods for systems of variational inequalities
On the Four Conjectures of G G Lorentz Type in Lρ^2[-a, a]
关于m-增生算子零点的粘性复合迭代序列的强收敛性
M/M^k,B/1算子的预解集
Strong convergence of an iterative algorithm for nonself multimaps in Banach spaces
Convergence analysis of a hybrid relaxed-extragradient method for monotone variational inequalities
Hybrid steepest descent methods for zeros of nonlinear operators with applications to variational in
Hybrid proximal point algorithms for solving constrained minimization problems in Banach spaces
一类拟线性椭圆方程的非平凡解
Banach空间中一类新的κ-次增生型变分包含问题解的迭代逼近
非扩张映像不动点的一种变形迭代算法
Banach空间中广义投影变形迭代法的收敛性
Banach空间中Φ-强拟压缩映射的Ishikawa迭代过程
有限多个集值映象公共不动点的修正的Mann迭代程序
一类拟线性椭圆变分不等式解的存在性
Iterative Schemes for a Family of Finite Asymptotically Pseudocontractive Mappings in Banach Spaces
关于一对集值映象和两对单值映象的公共不动点定理
Φ-压缩条件下6个映象的公共不动点定理
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