求解不等式约束非线性优化问题的信赖域SQP方法
Trust Region SQP Method for Solving Inequality Constrained Nonlinear Optimization Problems
DOI: 10.12677/AAM.2023.122067, PDF, HTML, 下载: 168  浏览: 281 
作者: 刘文杰, 范喜东：云南财经大学统计与数学学院，云南 昆明
关键词: 非线性优化问题；SQP优化方法；信赖域SQP优化方法；Nonlinear Optimization Problems； SQP Optimization Method； SQP Optimization Method of Trust Region
摘要: 针对不等式约束非线性优化问题求解上已经有了很多优化的方法，例如序列二次规划(SQP)方法， 而本文则是在SQP优化方法的基础上研究井建立的一个将信赖域方法与其结合的方法一一信赖域SQP方法，然后给出相应的实例对该算法进行数值实验模拟，井将其与原来的SQP方法进行比较。 最后得出在适当的条件下，信赖域SQP方法相较于原有的SQP方法具有更好的数值效果，数值的结果也一定程度上验证了这个算法的可行性。
Abstract: There have been many optimization methods for solving inequality constrained nonlin- ear optimization problems, such as sequential quadratic programming (SQP) method. In this paper, a method combining confidence region method with SQP method is studied and established on the basis of SQP optimization method-confidence region SQP method. Then the corresponding examples are given to simulate the algorithm and compare it with the original SQP method. Finally, under appropriate conditions, the confidence region SQP method has better numerical results than the original SQP method, and the numerical results also verify the feasibility of this algorithm to a certain extent.
文章引用：刘文杰, 范喜东. 求解不等式约束非线性优化问题的信赖域SQP方法[J]. 应用数学进展, 2023, 12(2): 634-644. https://doi.org/10.12677/AAM.2023.122067

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