一类新的求解约束优化问题的锥模型信赖域算法

A new trust region algorithm with conic model for constrained optimization

本文提出了一类新的求解线性等式约束优化问题的锥模型信赖域算法.不同于以往的求解约束问题的锥模型信赖域算法,无论试探步是否被接受,我们在每步都采用Wolfe线搜索得到下一个迭代点,避免了重解子问题,并且保证了序列{Bk}满足拟牛顿方程及其正定性.在适当条件下,证明了算法的全局收敛性,数值试验表明该算法是有效的.

In this paper,we present a new trust region method with conic model for linearly inequality constrained optimization. Different from traditional trust region algorithms,our algorithms gets the next point by the Wolfe line search at each iteration whether the trial step is accepted. This new algorithm not only does not resolve the subproblem but also satisfies the quasi-Newton condition at each iteration and simultaneously maintains a positive-definite approximation to the Hessian of the object function. Under mild conditions, we prove that global convergence of the algorithm. Numerical example show that the algorithm is effective.