On Interior-Point Warmstarts for Linear and Combinatorial Optimization

Despite the many advantages of interior-point algorithms over active-set methods for linear optimization, one of the remaining practical challenges is their current limitation to efficiently solve series of related problems by an effective warmstarting strategy. In its remedy, in this paper we present a new infeasible-interior-point approach to quickly re-optimize an initial problem instance after data perturbations, or a new linear programming relaxation after adding cutting planes for discrete or combinatorial problems. Based on the detailed complexity analysis of the underlying algorithm, we perform a comparative analysis to coldstart initialization schemes and present encouraging computational results with iteration savings around 50% on average for perturbations of the Netlib linear programs and successive LP relaxations of max-cut and the traveling-salesman problem.