Double-Regularization Proximal Methods, with Complementarity Applications
Computational Optimization and Applications
Computational Optimization and Applications
Variational Inequalities and Economic Equilibrium
Mathematics of Operations Research
Penalty approximation method for a class of elliptic variational inequality problems
Computers & Mathematics with Applications
An algorithm for generalized variational inequality with pseudomonotone mapping
Journal of Computational and Applied Mathematics
The interior proximal extragradient method for solving equilibrium problems
Journal of Global Optimization
An LQP-based descent method for structured monotone variational inequalities
Journal of Computational and Applied Mathematics
Exact penalties for variational inequalities with applications to nonlinear complementarity problems
Computational Optimization and Applications
An LQP-Based Decomposition Method for Solving a Class of Variational Inequalities
SIAM Journal on Optimization
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We consider a new class of multiplier interior point methods for solving variational inequality problems with maximal monotone operators and explicit convex constraint inequalities. Developing a simple Lagrangian duality scheme which is combined with the recent logarithmic-quadratic proximal (LQP) theory introduced by the authors, we derive three algorithms for solving the variational inequality (VI) problem. This provides a natural extension of the methods of multipliers used in convex optimization and leads to smooth interior point multiplier algorithms. We prove primal, dual, and primal-dual convergence under very mild assumptions, eliminating all the usual assumptions used until now in the literature for related algorithms. Applications to complementarity problems are also discussed.