一种基于信赖域约束的优化问题的求解方法

讨论一类仅含有线性约束条件的优化问题,在每次迭代过程中,用二次近似模型近似目标函数,从而构造一个子问题,以便于确定迭代方向.在每个子问题求解时引入一组共轭方向,子问题可以转化为一个线性规划问题和一个一维约束优化问题.为了保证算法的总体收敛性,应用信赖域算法代替一维搜索,确定下一个迭代点.证明了算法产生的点列如有聚点,则必有一个聚点是原问题的K-T点.

One method of solving constrained optimization problem basing on the trust-region

A method was proposed to solve constrained optimization problems with linear constraints in this paper.At each iterate,the objective function was approached by a quadratic model function for searching the iterated direction and a subproblem was created.The subproblem was transformed to a linear programming and a one-dimension constrained optimization problem by solving them with a group of conjuate direction.A trust-region methods which were replaced by line search methods were adopted to assure the global convergence.Finally,it was proved that if the sequence of vector generated by algorithm in this paper have many convergent points,one of them must be K-T.