非线性不等式约束最优化一个超线性与二次收敛的强次可行方法(英文)

A Superlinearly and Quadratically Convergent Strongly Subfeasible Method for Nonlinear Inequality Constrained Optimization

本文讨论非线性不等式约束最优化问题,借助于序列线性方程组技术和强次可行方法思想,建立了问题的一个初始点任意的快速收敛新算法。在每次迭代中,算法只需解一个结构简单的线性方程组。算法的初始迭代点不仅可以是任意的,而且不使用罚函数和罚参数,在选代过程中,迭代点列的可行性单调不减。在相对弱的假设下,算法具有较好的收敛性和收敛速度,即具有整体与强收敛性,超线性与二次收敛性。文中最后给出一些数值试验结果。

In this paper, nonlinear inequality constrained optimization problems are discussed. By using the technique of sequential systems of linear equations and strongly subfeasi-ble methods, we present a new fast convergent algorithm with arbitrary initial point. At each iteration, the new algorithm need only to solve one linear system with simple structure. The algorithm possesses the following properties: the initial point is arbitrary; Penalty function and parameter are not used; The feasibility of the iterative points is monotone nondecreasing during interative process. Under relatively weaker hypotheses, the algorithm possesses better convergence and rate of convergence, i.e. global and strong convergence, superlinear and quadratical convergence. Finally, some numerical results are given.