Mathematical Programming: Series A and B
On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B
Global methods for nonlinear complementarity problems
Mathematics of Operations Research
Approximate iterations in Bregman-function-based proximal algorithms
Mathematical Programming: Series A and B
A Logarithmic-Quadratic Proximal Method for Variational Inequalities
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
A Relative Error Tolerance for a Family of Generalized Proximal Point Methods
Mathematics of Operations Research
A Weak-to-Strong Convergence Principle for Fejé-Monotone Methods in Hilbert Spaces
Mathematics of Operations Research
Convergence of Proximal-Like Algorithms
SIAM Journal on Optimization
A Generalized Proximal Point Algorithm for the Variational Inequality Problem in a Hilbert Space
SIAM Journal on Optimization
Computational Optimization and Applications
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To solve nonlinear complementarity problems, the inexact logarithmic-quadratic proximal (LQP) method solves a system of nonlinear equations (LQP system) approximately at each iteration. Therefore, the efficiencies of inexact-type LQP methods depend greatly on the involved inexact criteria used to solve the LQP systems. This paper relaxes inexact criteria of existing inexact-type LQP methods and thus makes it easier to solve the LQP system approximately. Based on the approximate solutions of the LQP systems, a descent method, and a prediction---correction method are presented. Convergence of the new methods are proved under mild assumptions. Numerical experiments for solving traffic equilibrium problems demonstrate that the new methods are more efficient than some existing methods and thus verify that the new inexact criterion is attractive in practice.