一类混合束方法子问题的求解研究

Study on the Solution of a Hybrid Bundle Method Subproblem

摘要: 非光滑优化问题的求解一直以来都是优化理论的重点研究对象，本文提出了一类带有矩阵范数的混合束方法子问题，然后利用对偶空间理论研究该问题的Lagrange函数，最后通过对偶问题与原问题的关系，计算出该混合束方法子问题的解，并给出具体的表达式。

Abstract: The solutions of non-smooth optimization problem have been the focus of the optimization theory for a long time. This paper proposes a class of hybrid bundle method subproblem with matrix norm, and then researches this subproblem’s Lagrange function by taking advantage of the dual space theorem. Finally, based on relation between the dual problem and the original problem, the solution of hybrid bundle method subproblem is calculated, and the concrete expression is given.