位置：立项数据库 > 立项详情页
集值优化问题的最优性条件以及稳定性和灵敏性分析
  • 项目名称：集值优化问题的最优性条件以及稳定性和灵敏性分析
  • 项目类别：面上项目
  • 批准号：10871216
  • 申请代码：A011201
  • 项目来源：国家自然科学基金
  • 研究期限：2009-01-01-2011-12-31
  • 项目负责人：李声杰
  • 负责人职称：教授
  • 依托单位：重庆大学
  • 批准年度：2008
中文摘要：

本课题拟研究集值优化模型。首先，通过图像定义集值映射的各种高阶导数，研究集值优化问题带高阶导数的最优性条件以及高阶对偶问题。其次，通过类似向量值映射的Fréchet导数和支撑函数定义的集值映射的各种导数，研究集值优化问题以及集优化问题的最优性条件、扰动集值优化问题解集映射的上下半连续性、Lipschitz连续性以及H?lder连续性。同时，研究集值优化问题有效点扰动映射、真有效点扰动映射和弱有效点扰动映射的相依导数、原导数、半导数以及邻近导数的具体计算公式以及同目标空间中可行集映射所相对应的导数的有效点集、真有效点集和弱有效点集之间的包含关系。最后，研究带上下容量限制向量交通网络系统模型的均衡原理以及与向量变分不等式和标量变分不等式的关系。并借助于非线性标量函数和变分不等式的算法，得到它们的具体可行算法。这项工作对我国经济系统、通讯系统和国防系统的平衡与优化组合具有重大意义。

中文主题词： 集值优化；最优性条件；对偶；稳定性；灵敏性
结论摘要：

英文主题词Set-valued optimization;Optimality conditions;Duality;Stability;Sensitivity.

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 51
  • 0
  • 0
  • 0
  • 0
期刊论文
Hadamard well-posed vector optimization problems
Second-Order Differential and Sensitivity Properties of Weak Vector Variational Inequalities
HIGHER-ORDER SENSITIVITY ANALYSIS IN NONCONVEX VECTOR OPTIMIZATION
LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS
GENERALIZED HIGHER-ORDER OPTIMALITY CONDITIONS FOR SET-VALUED OPTIMIZATION UNDER HENIG EFFICIENCY
Vector equilibrium flows with nonconvex ordering relations
ON THE SOLUTION CONTINUITY OF PARAMETRIC GENERALIZED SYSTEMS
Existence of solutions for generalized vector quasi-equilibrium problems
Sufficient Conditions of Isolated Minimizers for Constrained Programming Problems
Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality
Higher-order optimality conditions for weakly efficient solutions in nonconvex set-valued optimizati
A minimax theorem for vector-valued functions in lexicographic order
A method of duality for a mixed vector equilibrium problem
On the solution semicontinuity to a parametric generalized vector quasivariational inequality
Conjugate Duality in Constrained Set-Valued Vector Optimization Problems
Holder continuity and upper estimates of solutions to vector quasiequilibrium problems
NONLINEAR AUGMENTED LAGRANGIAN FOR NONCONVEX MULTIOBJECTIVE OPTIMIZATION
Stability results for convex vector-valued optimization problems
Holder Continuity of Solutions to Parametric Weak Generalized Ky Fan Inequality
LEVITIN-POLYAK WELL-POSEDNESS OF GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS
Solution semicontinuity of parametric generalized vector equilibrium problems
ON DERIVATIVES OF THE GENERALIZED PERTURBATION MAPS
Conjugate dual problems in constrained set-valued optimization and applications
Higher order weak epiderivatives and applications to duality and optimality conditions
Different Conjugate Dual Problems in Vector Optimization and Their Relations
Levitin-Polyak well-posedness of vector equilibrium problems
Weak subdifferential for set-valued mappings and its applications
An Ekeland's variational principle for set-valued mappings with applications
Calculus Rules for Derivatives of Multimaps
A new proof approach to lower semicontinuity for parametric vector equilibrium problems
Well-posedness for set optimization problems
A robust SQP method based on a smoothing lower order penalty function
The Holder continuity of solutions to generalized vector equilibrium problems
Codifferential Calculus
Coderivatives of the generalized perturbation maps
Continuity of approximate solution mappings for parametric equilibrium problems
On vector variational-like inequalities and set-valued optimization problems
Second-Order Contingent Derivative of the Perturbation Map in Multiobjective Optimization
Sensitivity analysis of parametric weak vector equilibrium problems
Robinson metric regularity of parametric variational systems
Lower Studniarski derivative of the perturbation map in parametrized vector optimization
Error analysis of approximate solutions to parametric vector quasiequilibrium problems
HIGHER-ORDER GENERALIZED ADJACENT DERIVATIVE AND APPLICATIONS TO DUALITY FOR SET-VALUED OPTIMIZATION
广义高阶锥方向导数及对集值优化的应用
ε-strongly Efficient Solutions for Vector Optimization with Set-valued Maps
Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps
扰动广义向量变分不等式解的半连续性(英文)
向量值映射锥鞍点存在定理
集值优化问题Benson真有效解的高阶Fritz John型最优性条件
广义扰动映射的上导数
相关项目
向量优化的近似解研究
期刊论文 9
受限条件下贵金属团簇的稳定性与催化活性的关系
期刊论文 37
超空泡流动结构与稳定性研究
期刊论文 64 会议论文 19 获奖 4
考虑地基共同作用影响的大型储液罐体系稳定性研究
期刊论文 14 会议论文 4 专利 1
非光滑集值优化理论及其应用研究
期刊论文 32 会议论文 5
梁板壳动力分析的稳定子域积分高效无网格法研究
期刊论文 35 会议论文 11
基于上图技巧的DC鲁棒优化问题的对偶理论
期刊论文 17
蛋白质药物溶液稳定性的试验方法与理论基础
期刊论文 11
深埋地下洞室群围岩的变形机理与稳定性评判准则研究
期刊论文 22 会议论文 4
李声杰的项目
向量平衡问题以及像空间分析方法
向量优化问题中集值映射的连续性和微分性研究
期刊论文 73 获奖 1
在网络系统中多指标平衡问题的理论与方法研究
期刊论文 36