一类联合最大特征值函数优化问题

非光滑凸优化问题是运筹学的一类重要问题.束方法作为解决非光滑凸优化问题最有效的方法之一,已经被广泛地应用于各个领域.运用束方法对最大特征值函数与一般非光滑凸函数之和的优化问题进行研究.首先,对目标函数进行近似;其次,给出求解此类优化问题的带有罚项的束方法算法;最后,通过收敛性分析证明了算法产生的序列会收敛到原问题的最优解.

Solving a Minimization Problem for a Classof Joint Maximum Eigenvalue Functions

Nonsmooth convex optimization problem is methods are considered as one of the most efficient a class of important problems in operations research. Bundle methods for solving nonsmooth optimization problems. The methods have already been applied to ＇many practical problems. In this paper,The bundle method algorithm with a penalty parameter be given to solve the optimization problem which is a sum of a maximum eigenvalue function and a nonsmooth convex function. The objective function in the problem be approximated to a piecewise smooth function. The convergence results be proved that the sequence produced by the algorithm converge to the optimal solution of the original problem.