Papers by Keyword: Aggregate Function

Abstract: A method of multiplier is presented for solving optimization problems. For large-scale constraint problems, combining the active set strategy, we use the aggregate function to approximate the max-value function. Only a few of functions are involved at each iteration, so the computation for gradient is significantly reduced. The numerical results show that the method is effective.

Abstract: Min-max-min programming is an important but difficult nonsmooth programming. An aggregate homotopy method was given for solving min-max-min programming by Bo Yu el al. However, the method requires a difficult to verify weak-normal cone condition. Moreover, the method is only theoretically with no algorithmic implementation. In this paper, the weak normal cone condition is discussed first. A class of min-max-min programming satisfying the condition is introduced. A detailed algorithm to implement the method is presented. Models arising from some applications such as support vector machine for multiple-instance classification in data mining, can be included in the problem. In the end, the aggregate homotopy method is given to solve the multiple-instance support vector machine model.