基于次模函数极小化的最优化问题  

Optimization Problems Based on the Minimization of Sub-modular Functions

作　　者：邓素娟 

机构地区：[1]内江市第一中学,四川内江641199

出　　处：《内江师范学院学报》2016年第12期29-32,共4页Journal of Neijiang Normal University

摘　　要：提出将最优化问题的对偶间隙改写成函数的积分形式,即转化为次模函数极小化问题,再通过Lovász延拓来实现正则化.并实际讨论了基于最接近方法和多面体的最优化问题的次模函数的构造方法,从理论上证明了最优化问题与次模极小化问题之间的等价性关系.The idea of the duality gap of optimization problem being rewritten into an integral form of a function is put forth so that the problem is converted to a minimization problem of a sub-modular function. Then by use of Lovasz continuation the regularization is achieved. And the method for the construction of sub-modular function regarding the optimization problem is discussed on the basis of the proximal approach and polyhedron thus it is theoretically proven that there exists an equivalent relation between the optimization problem and the sub-modular minimization problem.

关 键 词：次模函数 最接近方法 多面体 最优化 等价性 

分 类 号：O174[理学—数学]