Reoptimization With the Primal-Dual Interior Point Method

Abstract

Re-optimization techniques for an interior point method applied to solve a sequence of linear programming problems are discussed. Conditions are given for problem perturbations that can be absorbed in merely one Newton step. The analysis is performed for both short-step and long-step feasible path-following method. A practical procedure is then derived for an infeasible path-following method. It is applied in the context of crash start for several large-scale structured linear programs. Numerical results with OOPS, a new object-oriented parallel solver, demonstrate the efficiency of the approach. For large structured linear programs crash start leads to about 40% reduction of the iterations number and translates into 25% reduction of the solution time. The crash procedure parallelizes well and speed-ups between 3.1-3.8 on 4 processors are achieved.

Advances in the simulation of viscoplastic fluid flows using interior-point methods

“…However, it is known that IPM cannot easily take advantage of a previously known solution as a good initial guess ("warm-start") as it is too close from the feasible region boundary and far from the new central path. Finding good warm-starting strategies for IPM is still an active research topic [42][43][44].…”

Cutting-set methods for robust convex optimization with pessimizing oracles

“…A general rule-of-thumb is that warm-start can reduce the effort per iteration by factor of up to 10 or so (for example, in the barrier method). For more on warm-starting and its benefits, see, e.g., [84,85].…”

An exact primal–dual penalty method approach to warmstarting interior-point methods for linear programming

“…Among them are Freund's shifted barrier method [7] to allow infeasibility of the nonnegative variables, Gondzio and Grothey's [9] and Yildirim and Wright's [23] storage of a nearly optimal, well-centered point, Lustig et.al. 's [16] perturbation of the problem to move the boundary, and Polyak's modified barrier function [19].…”

“…'s [16] perturbation of the problem to move the boundary, and Polyak's modified barrier function [19]. Of these papers, only [9] and [16] report numerical results, and only on a few classes of problems. The results show improvement over coldstarts.…”