求解合作对策解的带有正不定临界项的对称交替方向法

On Solution of Cooperative Game Based on Symmetric Alternating Direction Method with Positive Indefinite Proximal Regularization

主要研究合作对策解的问题:首先根据核心及Shapley值的特点引入了最公平核心的概念,再将最公平核心转化为具有线性约束的凸二次规划问题,最后运用带有正不定临界项的对称交替方向法对其求解.由于问题的可行域为简单闭凸集,因此算法是可行的.

In this paper, the solution of cooperative game has been considered. Firstly, the definition of the fairest core has been introduced according to the characteristics of the Core and the Shapley value. Secondly, the fairest core has been translated to the convex quadratic programming problem with linear constraint. Finally, the symmetric alternating direction method has been used with positive indefinite proximal regularization to solve the problem. Since the feasible domain is simple closed convex set, the algorithm can be computed.