求解隐混合变分不等式的黄金比算法

Golden ratio algorithm for solving implicit mixed variational inequalities

混合变分不等式是变分不等式的一种推广,在经济、工程、物理、力学和电子信息等领域均有广泛的应用.基于混合变分不等式问题,提出了隐混合变分不等式问题,并且研究了求解该问题的黄金比算法.在一定的假设条件下证明了算法产生的序列能够收敛到该问题的解.

Mixed variational inequality is a generalization of variational inequality,which finds wide application in the fields of economy,engineering,physics,mechanics,electronic information and so on.Based on the mixed variational inequality problem,the implicit mixed variational inequality problem is proposed,and the golden ratio algorithm for solving the problem is studied.Under certain assumptions,it is proved that the sequence generated by the golden ratio algorithm converges to the solution of the problem.