有界变量约束优化的非单调最优路径内点算法

A nonmonotonic interior point algorithm via optimal path for nonlinear optimization with bounds to variables

采用最优路径结合非单调内点回代算法解有界变量约束的非线性优化问题.从构建的最优路径解二次模型获得迭代方向,通过线搜索获得步长因子以保证迭代点既落在严格可行域内,又能使目标函数产生足够下降.基于导出的最优路径的良好性质,在合理的假设下,证明了此算法不仅具有整体收敛性,而且保持局部超线性收敛速率.引入非单调技术将克服病态问题,从而加速收敛性进程.数值计算表明了算法的可行性和有效性.

This paper proposes a nonmonotonic interior point algorithm via optimal path for nonlinear optimization subject to bounds to variables. Based on the properties of the optimal path, the iterative direction is obtained by solving the quadratic model via the path. Using the nonmonotonic line search technique, we find an acceptable trial step length along this direction which is strictly feasible and makes the objective function monotonically decreasing. Theoretical analyses are given which prove that the proposed algorithm is globally convergent and has a local superlinear convergence rate under some reasonable conditions. The nonmonotonic criterion is used to speed up the convergence progress in the contours of objective function with large curvature. Numerical results indicate that the algorithm is effective in practice.