科研之友
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摘要
As one of the operator splitting methods, the Peaceman-Rachford splitting method (PRSM) has attracted considerable attention recently. This paper proposes a generalized PRSM for structured variational inequalities with positive orthants. In fact, we apply the well-developed LQP regularization to regularize the subproblems of the recently proposed strictly contractive PRSM, thus the resulting subproblems reduce to two nonlinear equation systems, which are much easier to solve than the subproblems of PRSM. Furthermore, these two nonlinear equations are allowed to be solved inexactly. For the new method, we prove its global convergence and establish its worst-case convergence rate in the ergodic sense. Numerical experiments show that the proposed method is quite efficient for the traffic equilibrium problems with link capacity bound.
