仿射内点最优路径法解线性不等式约束的优化问题

Interior affine scaling curvilinear path algorithm for nonlinear optimizations subject to linear inequality constraints

提供了仿射内点回代技术的最优路径法解线性不等式约束的非线性优化问题.通过构造的最优路径得到搜索迭代方向,结合非单调内点回代线搜索技术获得可接受的步长因子,从而产生保证目标函数值非单调下降的严格内点可行迭代序列.基于最优路径的良好性质,证明了在合理的假设条件下,算法不仅具有整体收敛性而且保持超线性收敛速率.引入非单调技术能克服高度非线性的病态问题,加速收敛性进程.数值计算结果表明了算法的有效性.

We propose an interior affine scaling optimal path algorithm with nonmonotonic interior back - tracking technique for nonlinear optimization subject to linear inequality constraints. Using both optimal path search strategy and line search technique, the quadratic model at each iteration generates a backtracking step to obtain a new accepted step. The global convergence and fast local convergence rate of the proposed algorithm are established 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 useful and effective in practice.