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广义半无限规划的理论与算法研究
  • 项目名称：广义半无限规划的理论与算法研究
  • 项目类别：面上项目
  • 批准号：10571106
  • 申请代码：A011201
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2008-12-31
  • 项目负责人：王长钰
  • 负责人职称：教授
  • 依托单位：曲阜师范大学
  • 批准年度：2005
中文摘要：

半无限规划在经济均衡、最优控制、信息技术等领域有着广泛而直接的应用。随着高新技术的发展与社会经济的深刻变化，这些领域出现了许多广义半无限规划的数值模型，即模型中最优值函数的产生域已不再是紧致的常值集合而是非紧致集或是一个点到集映象。例如近年发展起来的广义Nash博弈就是一个广义半无限极大极小规划。对于半无限规划结构的这种实质性的扩展，有许多理论与计算方面的新课题需待解决，这即是本项研究的目标。具体说，我们针对Polak等人概括出的半无限规划的三类一般模型，来研究它们的广义模型(1)建立它们的最优性条件（最近我们已对广义半无限极大极小规划在它的产生域是非紧致集的情况下，建立了一阶最优性条件）。(2)建立它们的广义Lagrangian对偶定理与稳定性定理。(3) 建立它们的有效算法，并将算法应用于广义Nash均衡和鲁棒Nash均衡的求解。

中文主题词： 广义半无限规划;点到集映象;最优值函数;广义Lagrangian对偶;
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  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
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期刊论文
带扰动项的梯度法与混合投影法的收敛性分析
Dai-Yuan Conjugate Gradient Method with Linesearch in the presence of Error
Unified theory of augumented Lagrangian methods for constrained global optimization
求解拟变分不等式问题的一种投影算法
A Trust region algorithm with memory for equality constrained optimization
Global Convergence of the Dai-Yuan conjugate gradient method with perturbations
Convergence property of gradient-type methods with non-monotone line search in the presence of pertu
Solving semidefinite programming problems via alternating direction methods
Global convergence of modified HS conjugate gradient method
A new halfspace-relaxation projection method for the split feasibility problem
Convergence properties of the dependent PRP conjugate gradient methods
A Trust Region Method for Optimizxation problem with Singular Solutions
带扰动项的梯度法与混合投影法的收敛性分析,
Merit Function and Error Bound via SQP Method and their Applications
约束最优化问题中投影梯度的误差界及其应用
带扰动项的FR共轭梯度法
On the convergence of a new hybrid projection algorithm
A Class of Conjugate gradient methods with Armijo-type line searches
Convergence property of the three-term memory gradient method and its projection method
A method for solving nonlinear complementarity problems and its convergence properties
Convergence Properties of a Correlative Polak- Ribiere Conjugate Gradient Method
解带线性或非线性约束最优化问题的混合三项记忆梯度投影算法
一个新的带误差项的记忆梯度算法
A new nonmonotone line search technique for unconstrained optimizati optimization
Strong Global Convergence of an Adaptive Nonmonotone Memory Gradient Method
Convergence properties of inexact projected gradient methods
Global convergence properties of the two new dependent Fletcher-Reeves conjugate gradient methods
A Note On The Gradient Projection Method With Exact Stepsize Rule
Global convergence of a memory gradient method without line search
A Global Error Bound via the SQP Method for constrained Optimization Problem and Its Applications
Convergence properties of descent methods with errors
求解非线性系统的有效集信赖域方法
Global convergence of a modified gradient projection method for convex constrained problems
新非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法
大步长非单调线搜索规则的Lampariello修正对角稀疏拟牛顿算法的全局收敛性
Some projection-like Methods for the Generalized Nash Equilibria
Solving?a?class?of?generalized?semi-infinite? programming?via?augumented lagrangians
指数型增广Lagrangian函数在广义半无限规划中的应用
通过转化来求解广义半无限极大极小问题
On Saddle Points of a Alass of Augumented Lagrangian Functions
A smoothing Levenberg–Marquardt method for the extended linear complementarity problem
一类逼近精确罚函数的罚函数
Zero Duality Gap Properties for a Class of Lagrangian Dual Problem and the Convergence of its Optima
Saddle Points Theory of Two Classes of Augumented Lagrangians and Its Applications to Generalized Se
New Differential properties of sup-type funvtions
A relaxed extragradient-like method for a class of constrained optimization problem
Value Functions and Error Bounds of Trust Region Methods
Further insight into the Shamanskii modification of Newton method
A Global Error Bound of constrained Optimization Problem and Its Applications
Two Error Bounds for Constrained Optimization Problems and Their Applications
Solving bound constrained optimization via a new nonmonotone spectral projected gradient method
A hybrid method for the generalized Nash equilibria
On smoothing exact penalty functions for nonlinear constrained optimization problems
A Nonsmooth Levenberg-Marquardt Method for Solving Semi-Infinite Programming Problems
New Optimality Conditions for Generalized Semi-Infinite Min-Max Programming
A note on finite termination of iterative algorithms in mathematical programming
一类广义半无限规划问题的光滑牛顿算法
Zero duality and saddle points of a class of augmented Lagrangian functions in constrained non-conve
First-order Optimality Conditions for Convex Semi-infinite Min-Max Programming with Noncompact Sets
Properties of saddle points for generalized augumented Lagrangian
Unified Nonlinear Lagrangian Approach to Duality and Optimal Paths
结合广义Armijo步长搜索的带误差项的记忆梯度算法
修正的HS共轭梯度算法的全局收敛性
Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations
线搜索下带误差项的Dai—Yuan共轭梯度算法
一种新的带扰动项的算法的全局收敛性
带误差项的下降算法的收敛性
约束最优化问题中一个全局误差界及其应用
约束最优化问题中投影梯度的全局误差界及其应用
三项记忆梯度法及其投影算法的收敛性分析
一类Lagrangian对偶问题的零对偶间隙性质及其最优路径的收敛性
通过转化来求解广义半无限极大极小规划问题
广义半无限极大极小规划的一个新的最优性条件
一类新的自适应非单调谱投影梯度法
在Armijo型线搜索下共轭梯度法簇的全局收敛性
精确步长搜索下的梯度投影算法的收敛性与有限终止性
解决非线性互补问题非光滑牛顿算法的全局收敛以及局部收敛性分析
王长钰的项目
半无限规划的对偶理论与算法研究
期刊论文 8 会议论文 4 著作 58
最优值函数的方向可微性理论与约束最优化问题研究
期刊论文 1
数学规划的理论与算法研究
非线性增广Lagrangian函数的理论、方法与其应用研究
期刊论文 43