A Primal-Dual Slack Approach to Warmstarting Interior-Point Methods for Linear Programming

Despite the many advantages of interior-point algorithms over active-set methods for linear programming, one of their practical limitations is the remaining challenge to efficiently solve several related problems by an effective warmstarting strategy. Similar to earlier approaches that modify the initial problem by shifting the boundary of its feasible region, the contribution of this paper is a new but relatively simpler scheme which uses a single set of new slacks to relax the nonnegativity constraints of the original primal-dual variables. Preliminary computational results indicate that this simplified approach yields similar improvements over cold starts as achieved by previous methods.