Crash start of interior point methods

Crash start of interior point methods

The starting point used by an interior point algorithm for linear and convex quadratic programming may significantly influence the behaviour of the method. A widely used heuristic to construct such a point consists of dropping variable nonnegativity constraints and computing a solution which minimizes the Euclidean norm of the primal (or dual) point while satisfying the appropriate primal (or d...

Warm start by Hopfield neural networks for interior point methods

Hopfield neural networks and interior point methods are used in an integrated way to solve linear optimization problems. The Hopfield network gives warm start for the primal–dual interior point methods, which can be way ahead in the path to optimality. The approaches were applied to a set of real world linear programming problems. The integrated approaches provide promising results, indicating ...

Warm-Start Strategies in Interior-Point Methods for Linear Programming

We study the situation in which, having solved a linear program with an interiorpoint method, we are presented with a new problem instance whose data is slightly perturbed from the original. We describe strategies for recovering a \warm-start" point for the perturbed problem instance from the iterates of the original problem instance. We obtain worst-case estimates of the number of iterations r...

Interior-point Methods

Interior-Point Methods

The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming. In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semide nite programming, and nonconvex and nonlinear problems, have reached varyin...