论文标题
非线性程序的全球和局部融合的原始双重内点放松方法
A primal-dual interior-point relaxation method with global and rapidly local convergence for nonlinear programs
论文作者
论文摘要
基于求解经典对数轰炸子问题的等效参数限制的迷你最大问题，我们为非线性程序提供了一种新型的原始偶发性内点弛豫方法，该方法具有一般平等和非负相等约束的非线性程序。在每次迭代中，我们的方法近似求解了参数相等的Mini-Max子问题的KKT系统，这避免了任何原始或双重迭代的要求是内部。该方法与放松内点需求的热门内点方法具有一些相似之处，并且很容易扩展以解决一般不等式约束的问题。特别是，它有可能规避许多内部方法的障碍难度，而这些内点方法对于非线性程序而言，并改善了由于屏障参数很小而改善现有原始偶发性内点方法的不良条件。引入了一种新的平滑方法，以开发我们的放松方法并促进该方法的收敛。在适当的条件下，证明我们的方法可以是全球收敛的，并且可以在局部四边形地收敛到原始问题的KKT点。关于一个良好的问题的初步数值结果，许多内部点方法无法找到最小化器和一组可口收集的测试问题，表明我们的方法是有效的。
Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs with general equality and nonnegative constraints. In each iteration, our method approximately solves the KKT system of a parametric equality constrained mini-max subproblem, which avoids the requirement that any primal or dual iterate is an interior-point. The method has some similarities to the warmstarting interior-point methods in relaxing the interior-point requirement and is easily extended for solving problems with general inequality constraints. In particular, it has the potential to circumvent the jamming difficulty that appears with many interior-point methods for nonlinear programs and improve the ill conditioning of existing primal-dual interior-point methods as the barrier parameter is small. A new smoothing approach is introduced to develop our relaxation method and promote convergence of the method. Under suitable conditions, it is proved that our method can be globally convergent and locally quadratically convergent to the KKT point of the original problem. The preliminary numerical results on a well-posed problem for which many interior-point methods fail to find the minimizer and a set of test problems from the CUTEr collection show that our method is efficient.
