几类新型目标罚函数理论与算法研究

项目名称： 几类新型目标罚函数理论与算法研究

项目编号： No.11271329

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 孟志青

作者单位： 浙江工业大学

项目金额： 50万元

中文摘要： 本项目将针对单目标规划、互补约束规划和双层规划等约束优化问题，在已有的研究基础之上深入研究下面几类新型目标罚函数理论与算法：(1)研究单目标规划和双层规划问题的障碍目标罚函数理论与算法，包括等价性、近似精确性、算法及收敛性等，(2)研究单目标规划和双层规划的增广拉格朗日目标罚函数理论与算法：包括等价性、对偶性、算法及收敛性等，(3)研究互补约束规划和双层规划问题的互补约束目标罚函数理论与算法：包括等价性、精确性、算法及收敛性等。本项目的研究成果将对于解决单目标规划、互补约束规划和双层规划等问题具有十分重要的意义。

中文关键词： 目标罚函数算法；约束优化问题；障碍目标罚函数；增广拉格朗日目标罚函数；约束互补问题目标罚函数

英文摘要： Based on the existing theories, the project will study theories and algorithms of several new objective penalty functions for constrained optimization problems of single-objective programming, mathematical programs with complementary constraints and bilevel programming. It will (1) study theories and algorithms of obstacle objective penalty functions for single-objective programming and bilevel propramming, covering the equality, approximation exactness, algorithm and convergence; (2) study theories and algorithms of augmented Lagrangian objective penalty functions for single-objective programming and bilevel propramming, covering the equality, duality, algorithm and convergence; (3) study theories and algorithms of complementary constrained objective penalty functions for mathematical programs with complementary constraints, covering the equality, exactness, algorithms and convergence. The project's research results will have great significance in solving single-objective programming, mathematical programs with complementary constraints and bilevel programming.

英文关键词： Objective penalty function algorithm；constrained optimization problem；barrier objective penalty function；augmented Lagrange objective penalty function；constrained complementary objective penalty functi