线性不等式约束优化问题的仿射内点信赖域子空间算法

使用仿射变换内点回代技术的信赖域子空间算法解线性不等式约束的非线性优化问题．通过构造一个二维子空间，在子空间中求解信赖域的子问题得到迭代方向，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．子空间技术的应用使得该方法适用于求解大规模问题．在合理的假设条件下，给出了信赖域子空间算法的良好性质，从而保证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 subspace trust region method for nonlinear optimizations subject to linear inequality constraints

We present an affine scaling trust region algorithm with interior back - tracking and subspacc techniques for nonlinear optimizations subject to linear inequality constraints. Employing the subspace method, the trust region method and the interior back - tracking line search technique, we obtain an acceptable step length which is strictly feasible and makes the objective function monotonically decreasing. Due to the special structure of the subspace technology, the method can be applied to very large scale problems. The global convergence and fast local convergence rate of the proposed method are established under some reasonable conditions, Numerical results indicate that the method is effective.