一种极小化两个凸函数之和的混合近似邻近点算法

A Hybrid Approximate Proximal Point Algorithm for Minimizing the Sum of Two Convex Function

本文提出一种混合近似邻近点算法以求解极小化两个凸函数之和的无约束优化问题。通过将邻近点算法中的优化问题转化为一系列极小化近似函数的子问题来求解,以得到此优化问题的最优解。在子问题中用线性模型来取代原问题目标函数中非线性程度较低的函数,而在下一个子问题中,用二次模型来取代非线性程度较高的函数,进行交替运算。在临近点算法的框架下,求出原问题的解。最后给出3个算例以说明本文所给出的算法是有效的。

In this article, hybrid approximate proximal point algorithm is proposed to minimize the sum of two convex functions. It replaces the optimization problem in the proximal point algorithm by a series of subproblems of minimizing the approximate function to get the optimal solution of optimization problem. In the subproblems, the function with less nonlinearity is replaced by its linear model and the other is replaced by its quadratic model alternately. Under the framework of the proximal point algorithm, we can find tile solution of the original problem. Three numerical examples are given to illustrate the effectiveness of the present algorithm.