506 research outputs found
Data sets of very large linear feasibility problems solved by projection methods
We give a link to a page on the Web on which we deposited a set of eight huge
Linear Programming (LP) problems for Intensity-Modulated Proton Therapy (IMPT)
treatment planning. These huge LP problems were employed in our recent research
and we were asked to make them public.Comment: 4 pages, 1 tabl
A strongly polynomial algorithm for generalized flow maximization
A strongly polynomial algorithm is given for the generalized flow
maximization problem. It uses a new variant of the scaling technique, called
continuous scaling. The main measure of progress is that within a strongly
polynomial number of steps, an arc can be identified that must be tight in
every dual optimal solution, and thus can be contracted. As a consequence of
the result, we also obtain a strongly polynomial algorithm for the linear
feasibility problem with at most two nonzero entries per column in the
constraint matrix.Comment: minor correction
A Sampling Kaczmarz-Motzkin Algorithm for Linear Feasibility
We combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. We obtain a family of algorithms that generalize and extend both projection-based techniques. We prove several convergence results, and our computational experiments show our algorithms often outperform the original methods
The tropical shadow-vertex algorithm solves mean payoff games in polynomial time on average
We introduce an algorithm which solves mean payoff games in polynomial time
on average, assuming the distribution of the games satisfies a flip invariance
property on the set of actions associated with every state. The algorithm is a
tropical analogue of the shadow-vertex simplex algorithm, which solves mean
payoff games via linear feasibility problems over the tropical semiring
. The key ingredient in our approach is
that the shadow-vertex pivoting rule can be transferred to tropical polyhedra,
and that its computation reduces to optimal assignment problems through
Pl\"ucker relations.Comment: 17 pages, 7 figures, appears in 41st International Colloquium, ICALP
2014, Copenhagen, Denmark, July 8-11, 2014, Proceedings, Part
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