非线性规划问题的一种高效数值算法

A Effective Algorithm for Solving a Class of Non-Convex Optimization Problems

提出求解一类非线性规划问题的有效数值算法,利用新引入的映射代替约束函数的梯度,在较弱的条件下,给出算法的收敛性证明.应该指出的是,结果在很大程度上改进了已有的结果,使得该算法能够处理更大一类非凸优化问题.

In this paper, we propose a homotopy interior point method for solving a class of non-convex optimization problems. By using newly introduced mappings instead of the gradi- ents of constraint functions, we construct a new homotopy equation. Under weak assumptions, we give a constructive proof for the convergence of the method. It should be pointed out that our results improve the previous ones greatly, so that we can deal with a broader class of non-convex optimization problems.