An LQP-SQP alternating direction method for solving variational inequality problems with separable structure
Authors
Adnan Alhomaidan
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Abdellah Bnouhachem
- Laboratoire d'Ingénierie des Systèmes et Technologies de l'Information, Ibn Zohr University, Agadir, BP 1136, Morocco
Abdul Latif
- Department of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
Abstract
In this paper, by combining the
logarithmic-quadratic proximal (LQP) method and the square
quadratic proximal (SQP) method, we propose an inexact
alternating direction method for solving constrained variational
inequalities \(VI(S,f),\) where \(S\) is a convex set with linear
constraints.
Under certain conditions, the global
convergence of the proposed method is established. We show the
O(1/t) convergence rate for the inexact LQP-SQP alternating
direction method. To demonstrate the efficiency of the proposed
method, we provide numerical results for traffic equilibrium
problems.
Keywords
- Proximal point algorithm
- logarithmic-quadratic proximal method
- square quadratic proximal
- variational inequality
- prediction-correction
- traffic equilibrium problems
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