Robert M. Freund

TL;DR: In this paper, the authors present an algorithm for solving a linear program LP (to a given tolerance) from a given prespecified starting point, whose complexity depends explicitly and only on how close the starting point is to the set of LP feasible and optimal solutions.

TL;DR: In this paper, the authors used the NETLIB suite of linear optimization problems as a test bed for condition number computation and analysis, and showed that the number of IPM iterations needed to solve the problems in the NetLIB suite varies roughly linearly with log C(d) of the post-processed problem instances.

TL;DR: In this article, the problem of following a trajectory from an infeasible starting point directly to an optimal solution of the linear programming problem is studied. And the main thrust of the paper is the development of an algorithm that traces a given β-balanced trajectory from a starting point near the trajectory to an approximate optimal solution to the given linear program problem in polynomial time.

TL;DR: Computational results indicate that this methodology holds the promise to markedly reduce the overall computation time for conic feasibility problems; for instance, a 46% decrease in average IPM iterations for 100 randomly generated poorly-behaved problem instances of dimension 1000 x 5000 is observed.

TL;DR: In this article, an extension of the Frank-Wolfe method was proposed to induce near-optimal solutions on low-dimensional faces of the feasible region, where the in-face directions always keep the next iteration within the minimal face containing the current iterate.