一种求解约束条件下多变量非线性函数所有全局最优解的区间算法

一种求解约束条件下多变量非线性函数所有全局最优解的区间算法 An Interval Algorithm for Finding all Global Minimizers of a Constrained Nonlinear Function with Several Variables 李爽 LI Shuang 1 2 first-author 许才军 XU Cai-jun 1 2 王新洲 WANG Xin-Zhou) 1 2 武汉大学测绘学院 武汉大学测绘学院 School of Geodesy and Geomatics, Wuhan University School of Geodesy and Geomatics, Wuhan University 武汉大学测绘学院,湖北,武汉,430079 武汉大学测绘学院,湖北,武汉,430079 研究和实践中经常会遇到附有约束条件的非线性优化问题,对这类问题,通常采用随机搜索的方法来解决,但是,随机搜索法不能证明所得到的解就是全局最优解.本文给出了一种求解约束条件下非线性优化问题所有全局最优点和最优值的区间算法,该算法非常宜于解决优化问题,它能求出问题的所有全局最优解,给出解的包含区间,并很容易获得解的逼近误差,这是随机搜索等其他方法做不到的.理论分析和数值结果均表明,区间算法是稳定而可靠的. It is frequently the case that a mathematical model of a system contains limitations on the acceptable values of the parameters. This leads to the most general global optimization topic, namely the global nonlinear constrained optimization problem. General, the random search is used to solve this kind of problem. But the random algorithms can’t test if it’s result is the optimum of problem. An interval algorithm is established in this paper. This algorithm can solve the global nonlinear constrained optimization problem and is very suitable to solve optimization problem. It can find all global optimums and all global optimizers of the problem, and the inclusion interval of optimizers is output. By these intervals, the approaching errors can be gotten easily. This can’t be done by the others algorithms, such as the random search method. Both theory and numerical analysis show that this algorithm is stable and reliable. 区间算法 全局约束最优 非线性函数 interval algorithm global constrained optimization nonlinear function O174 国家自然科学基金项目（49904001）;高等学校骨干教师资助计划资助（2123） 2003-05-01 2021-04-01 5