非凸优化的近似束方法及对偶问题  

An Approximate Bundle Method for Non-convex Optimization and Its Dual Problem

作　　者：沈洁[1] 刘晓倩[1] 陈颖[1] 金希[1] 

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《重庆师范大学学报（自然科学版）》2016年第1期1-5,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.11301246)

摘　　要：束方法目前是解决非光滑优化问题最有前景的方法之一。出于实际计算的需要,使用两个扰动函数共同控制真实目标函数,利用它们的信息构建增广函数,从而把凸优化迫近束方法应用到非凸问题中来。类似地建立目标函数的下近似模型,通过求解二次规划最小值点作为下一个候选点,进一步再筛选出下降点。最后利用Lagrange函数写出了束方法子问题的对偶问题,揭示了扰动后原问题的最优解和对偶问题最优解之间的关系。Proximal bundle method is considered to be one of the most promising methods for solving non-smooth optimization problems. In this paper, due to the requirement of practical calculations, two disturbance functions are used to control the real objective function together, whose information is utilized to construct an augmented function. Thereby bundle method for convex optimization is applied to non-convex optimization problem. Similarly, lower approximate model of the objective function can be constructed and by solving quadratic programming, we expect to find out the minimum point as next candidate point, and furthermore select the decreased point. Finally, the dual problem of sub-problem of bundle method is given by utilizing Lagrange function, and at the same time the relation between the solutions of the primal problem which has been disturbed and the dual problem is also revealed.

关 键 词：非凸非光滑优化 束方法 近似函数值 Lagrange对偶问题 lower-C2函数 

分 类 号：O221.2[理学—运筹学与控制论]