求解非线性规划的修正滤子信赖域方法

苏珂, 刘英

数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1157-1164.

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数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1157-1164. DOI: 10.12386/A2009sxxb0144
论文

求解非线性规划的修正滤子信赖域方法

    苏珂1,2, 刘英1
作者信息 +

A Modified Filter Trust Region Method for Nonlinear Programming

    Ke SU1,2, Ying LIU1
Author information +
文章历史 +

摘要

在求解非线性规划问题的方法中, 序列二次规划型方法是最有效的求解方法之一. 而最近又出现了一类新的称为滤子的方法, 因为该方法有着良好的数值结果, 近年来已经广泛应用 于非线性规划问题的求解中. 在这篇文章中, 提出了一类组合了该滤子技巧和上述SQP信赖域技巧的方法来解决非线性规划问题. 该方法保证了每个试探点都不会远离可行域. 同时在合适的条件下建立了算法的收敛性, 并在最后给出了一些数值算例.

 

Abstract

Sequential quadratic programming (SQP) type method is one of the most effective methods for solving nonlinear programming. Recently, filter method, for its good numerical results, are extensively studied to handle nonlinear programming problems. In this paper, a new modified approach combined the filter technique and SQP trust region method is proposed to tackle the original problem, which ensures that every trail point will not be far away from the feasible region. Global convergence results of the proposed algorithm are established under suitable conditions. Some numerical results are reported in this paper.

 

关键词

滤子技巧 / 信赖域 / 序列二次规划 / 非线性规划

Key words

filter method / trust region / sequential quadratic programming / Nonlinear programming

引用本文

导出引用
苏珂, 刘英. 求解非线性规划的修正滤子信赖域方法. 数学学报, 2009, 52(6): 1157-1164 https://doi.org/10.12386/A2009sxxb0144
Ke SU, Ying LIU. A Modified Filter Trust Region Method for Nonlinear Programming. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1157-1164 https://doi.org/10.12386/A2009sxxb0144

参考文献


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基金

国家自然科学基金资助项目(10771162,60974134);河北大学自然科学基金资助项目(2009159)

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