求解不等式约束优化问题的SQP滤子算法  

The SQP Filter Algorithm for Solving Inequality Constrained Optimization Problem

作　　者：鲍勇[1] 范玉妹[1] 赵金玲[1] 

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《中北大学学报（自然科学版）》2014年第1期15-18,24,共5页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学(青年)基金资助项目(11101028);中央高校基本科研业务费专项资助项目(FRF-BR-11-001A)

摘　　要：序列二次规划(Sequential Quadratic Programming,SQP)方法是求解非线性规划问题最有效的方法之一,但是该方法与信赖域技术结合之后可能会导致二次规划(Quadratic Programming,QP)子问题不相容.对于此种现象,利用M.J.D.Powell提出的对QP子问题的约束条件引入变量的罚函数方法进行处理.计算出试探步,并用滤子接受准则选择是否接受试探步.对于完全牛顿步不被滤子接受的情况,计算二阶校正(Second Order Correction,SOC)步,使得其容易被滤子接受.在一定的条件下,算法具有全局收敛性,最后的数值试验也表明了算法是有效的.Abstract： Sequential Quadratic Programming （SQP） method is one of the most effective ways to solve a non- linear programming problem, but it may result in the incompatibility of Quadratic Programming （QP） sub- problem if the method is combined with the trust region technique. For this phenomenon, Powell proposed the penalty function method by introducing variable for the constraint condition of QP subproblem,and it was used to deal with this problem. The test steps were calculated, and whether accept test steps or not was chose by the filter acceptance criteria. If the unit step was not accepted by the filter, the Second Order Correction （SOC） step was calculated to make it easy to be accepted by the filter. Under certain conditions, the algo- rithm has global convergence, finally the numerical experiments also show that the algorithm is effective.

关 键 词：约束优化 QP子问题 信赖域 滤子 全局收敛性 

分 类 号：O221.2[理学—运筹学与控制论]