不等式约束优化一个新型可行QP-free算法

本文对非线性不等式约束优化问题提出了一个新的可行 QP-free 算法. 新算法保存了现有算法的优点, 并具有以下特性: (1) 算法每次迭代只需求解三个具有相同系数矩阵的线性方程组, 计算量小; (2) 可行下降方向只需通过求解一个线性方程组即可获得, 克服了以往分别求解两个线性方程组获得下降方向和可行方向, 然后再做凸组合的困难;(3) 迭代点均为可行点, 并不要求是严格内点; (4) 算法中采用了试探性线搜索,可以进一步减少计算量; (5) 算法中参数很少,数值试验表明算法具有较好的数值效果和较强的稳定性.

A NEW TYPE FEASIBLE QP-FREE ALGORITHM FOR INEQUALITY CONSTRAINED OPTIMIZATION

In this paper,a new feasible QP-free algorithm for solving the nonlinear optimization problems with inequality constraints is presented.It reserves all the advantages of previous algorithms,and the interesting features of the algorithm are summarized as follows:(1)At each iteration,only three systems of linear equations with the same coefficient matrix need to be solved,which decreases largely the amount of computations;(2)A feasible descent direction can be obtained by solving only one system of linear equations,while the previous algorithms need to solve one linear system to get a feasible direction and another one to obtain a descent direction,and an improving direction is obtained by doing a convex combination; (3)The iteration points are all feasible without requiring to be strictly interior points; (4)The exploratory fine search is introduced to the algorithm,and the computational cost can be further reduced;(5)The parameters in the proposed algorithm are few,and some numerical results illustrate that the proposed algorithm is efficient and stable.