Given an n n matrix M, a vector q in IR n , and a polyhedral convex set X = fxjAx b; Bx = dg, where A is an m n matrix and B is an p n matrix, the aane variational inequality problem is to nd x 2 X such that (Mx + q) T (y ? x) 0 for all y 2 X. If M is positive semi-deenite, the aane variational inequality can be transformed to a generalized complementarity problem, which can be solved in polyno...

In this report, we consider the problem of nding the maximum-volume ellipsoid inscribing a given full-dimensional polytope in < n deened by a nite set of aane inequalities. We present several formulations for the problem that may serve as algorithmic frameworks for applying interior-point methods. We propose a practical interior-point algorithm based on one of the formulations and present preli...

Due to recent advances in the development of linear programming solvers, some of the formerly considered difficult multicommodity problems can today be solved in few minutes, even faster than with specialized methods. However, for other kind of multicommodity instances, general linear solvers can still be quite inefficient. In this paper we will give an overview of the current state-of-the-art ...

In this paper, we discuss a polynomial and Q-subquadratically convergent algorithm for linear complementarity problems that does not require feasibility of the initial point or the subsequent iterates. The algorithm is a modiication of the linearly convergent method of Zhang and requires the solution of at most two linear systems with the same coeecient matrix at each iteration.

With the increasing power of computers, real-time algorithms tends to become more complex and therefore require better guarantees of safety. Among algorithms sustaining autonomous embedded systems, model predictive control (MPC) is now used to compute online trajectories, for example in the SpaceX rocket landing. The core components of these algorithms, such as the convex optimization function,...

In this paper we propose an efficient distributed algorithm for solving loosely coupled convex optimization problems. The algorithm is based on a primal-dual interior-point method in which we use the alternating direction method of multipliers (ADMM) to compute the primal-dual directions at each iteration of the method. This enables us to join the exceptional convergence properties of primal-du...

1. Abstract The complementarity problem consists in finding x ∈ IR such that x ≥ 0 , F (x) ≥ 0 and xF (x) = 0, where F : IR → IR. Complementarity problems are involved in several applications in engineering, economy and different branches of physics . We mention contact problems and dynamics of multiple bodies systems in solid mechanics. In this paper we present a new feasible interior point al...

We present an interior-point trust-funnel algorithm for solving large-scale nonlinear optimization problems. The method is based on an approach proposed by Gould and Toint (Math. Prog., 122(1):155196, 2010) that focused on solving equality constrained problems. Our method is similar in that it achieves global convergence guarantees by combining a trust-region methodology with a funnel mechanism...

Penalty and interior-point methods for nonlinear optimization problems have enjoyed great successes for decades. Penalty methods have proved to be effective for a variety of problem classes due to their regularization effects on the constraints. They have also been shown to allow for rapid infeasibility detection. Interior-point methods have become the workhorse in large-scale optimization due ...