On the existence of weak solutions for degenerate systems of variational inequalities with critical growth
We prove the existence of solutions to systems of degenerate variational inequalities.
On the generalized strongly nonlinear implicit variational inequalities in reflexive Banach spaces
On the implicit programming approach in a class of mathematical programs with equilibrium constraints
On the nonlinear implicit complementarity problem.
On the velocity projection map for polyhedral Skorokhod problems.
On Tridiagonal Linear Complementary Problems.
Operator-splitting methods for general mixed variational inequalities.
Parametric set-valued vector quasi-equilibrium problems.
Path following methods for steady laminar Bingham flow in cylindrical pipes
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
Path following methods for steady laminar Bingham flow in cylindrical pipes
This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...
Perturbed iterative algorithms with errors for completely generalized strongly nonlinear implicit quasivariational inclusions.
Projective algorithms for solving complementarity problems.
Pseudomonotonicity and related properties in Euclidean Jordan algebras.
Quasivariational inequalities for a dynamic competitive economic equilibrium problem.
Regularization method for stochastic mathematical programs with complementarity constraints
In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions.
Regularization method for stochastic mathematical programs with complementarity constraints
In this paper, we consider a class of stochastic mathematical programs with equilibrium constraints (SMPECs) that has been discussed by Lin and Fukushima (2003). Based on a reformulation given therein, we propose a regularization method for solving the problems. We show that, under a weak condition, an accumulation point of the generated sequence is a feasible point of the original problem. We also show that such an accumulation point is S-stationary to the problem under additional assumptions....
Rescaled proximal methods for linearly constrained convex problems
We present an inexact interior point proximal method to solve linearly constrained convex problems. In fact, we derive a primal-dual algorithm to solve the KKT conditions of the optimization problem using a modified version of the rescaled proximal method. We also present a pure primal method. The proposed proximal method has as distinctive feature the possibility of allowing inexact inner steps even for Linear Programming. This is achieved by using an error criterion that bounds the subgradient...
Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality
Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...
Saddle point problems, bilevel problems, and mathematical program with equilibrium constraint on complete metric spaces.
Sensitivity analysis for variational inclusions by Wiener-Hopf equation techniques.