Interior point methods and random walk approaches have been long considered disparate approaches for convex optimization. We show how simulated annealing, one of the most common random walk algorithms, is equivalent, in a certain sense, to the central path interior point algorithm applied to the entropic universal barrier function. Using this observation we improve the state of the art in polyn...

Cutting plane methods require the solution of a sequence of linear programs where the solution to one provides a warm start to the next A cutting plane algorithm for solving the linear ordering problem is described This algorithm uses the primal dual interior point method to solve the linear programming relaxations A point which is a good warm start for a simplex based cutting plane algorithm i...

 Abstract  We consider an application of the ABS procedure to the linear systems arising from the primal-dual interior point methods where Newton method is used to compute path to the solution. When approaching the solution the linear system, which has the form of normal equations of the second kind, becomes more and more ill conditioned. We show how the use of the Huang algorithm in the ABS cl...

Most existing interior-point methods for a linear complementarity problem (LCP) require the existence of a strictly feasible point to guarantee that the iterates are bounded. Based on a regularized central path, we present an infeasible interior-point algorithm for LCPs without requiring the strict feasibility condition. The iterates generated by the algorithm are bounded when the problem is a ...

We present a parallel interior point algorithm to solve block structured linear programs. This algorithm can solve block diagonal linear programs with both side constraints (common rows) and side variables (common columns). The performance of the algorithm is investigated on uncapacitated, capacitated and stochastic facility location problems. The facility location problems are formulated as mi...

We present a predictor{corrector non{interior path following algorithm for the monotone linear complementarity problem based on Chen{Harker{Kanzow{Smale smoothing techniques. Although the method is modeled on the interior point predictor{ corrector strategies, it is the rst instance of a non{interior point predictor{corrector algorithm. The algorithm is shown to be both globally linearly conver...

It is an open question whether there is an interior-point algorithm for linear optimization problems with a lower iteration-complexity than the classical bound O( √ n log(1 μ0 )). This paper provides a negative answer to that question for a variant of the Mizuno-Todd-Ye predictor-corrector algorithm. In fact, we prove that for any > 0, there is a redundant Klee-Minty cube for which the aforemen...

The paper presents an algorithm for solving nonlinear programming problems. The algorithm is based on the combination of interior and exterior point methods. The latter is also known as the primaldual nonlinear rescaling method. The paper shows that in certain cases when the interior point method (ipm) fails to achieve the solution with the high level of accuracy, the use of the exterior point ...

In this section we will give an (extremely) brief Introduction to the concept of interior point methods • Logarithmic Barrier Method • Method of Centers We have previously seen methods that follow a path On the boundary of the feasible region (Simplex). As the name suggest, interior point methods instead Follow a path through the interior of the feasible region.