In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the quadratic program is the relaxation of a binary quadratic problem.

We propose QPALM, a nonconvex quadratic programming (QP) solver based on the proximal augmented Lagrangian method. This method solves sequence of inner subproblems which can be enforced to strongly convex and therefore admit unique solution. The resulting steps are shown equivalent inexact point iterations extended-real-valued cost function, allows for fairly simple analysis where convergence s...

Nonlinear rescaling (NR) methods alternate finding an unconstrained minimizer of the Lagrangian for the equivalent problem in the primal space (which is an infinite procedure) with Lagrange multipliers update. We introduce and study a proximal point nonlinear rescaling (PPNR) method that preserves convergence and retains a linear convergence rate of the original NR method and at the same time d...

Here we present a new approach to calculating the square root of a quadratic matrix. Actually, the purpose of this article is to show how the Cayley-Hamilton theorem may be used to determine an explicit formula for all the square roots of $2times 2$ matrices.

Abstract This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm damped semismooth Newton method. The outer regularization yields numerically stable method, we interpret operator as unconstrained minimization of augmented Lagrangian function. allows inner scheme to exploit sparse symmetric linear solvers m...

We present new abelian partial difference sets and amorphic group schemes of both Latin square type and negative Latin square type in certain abelian p-groups. Our method is to construct what we call pseudo-quadratic bent functions and use them in place of quadratic forms. We also discuss a connection between strongly regular bent functions and amorphic group schemes.