线性不等式约束优化问题的仿射内点不定dogleg算法

使用仿射变换内点回代技术的不定dogleg算法解线性不等式约束的非线性优化问题．通过对构造的仿射不定dogleg路径进行搜索得到迭代方向,结合线搜索内点回代技术获得可接受的步长因子,产生保证目标函数值单调下降的严格内点可行迭代序列．在合理的假设条件下。给出了不定dogleg路径的良好性质,从而证明了算法不仅具有整体收敛性,而且保持超线性收敛速率．数值计算结果表明了算法的有效性．

An interior affine scaling indefinite dogleg path algorithm for nonlinear optimizations subject to linear inequality constraints

We propose an affine scaling indefinite dogleg path algorithm with interior back - tracking technique for nonlinear optimizations subject to linear inequality constraints. Employing the indefinite dogleg path search strategy and interior back - tracking line search technique, we obtain an acceptable step length which is strictly feasible and makes the objective function monotonically decreasing. The global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions. Numerical results indicate that the algorithm is useful and effective in practice.