Clique-circulants and the stable set polytope of fuzzy circular interval graphsSpringer Science and Business Media LLC - Tập 115 - Trang 291-317 - 2007
Gianpaolo Oriolo, Gautier Stauffer
In this paper, we give a complete and explicit description of the rank facets of the stable set polytope for a class of claw-free graphs, recently introduced by Chudnovsky and Seymour (Proceedings of the Bristish Combinatorial Conference, 2005), called fuzzy circular interval graphs. The result builds upon the characterization of minimal rank facets for claw-free graphs by Galluccio and Sassano (J...... hiện toàn bộ
Breaking symmetries to rescue sum of squares in the case of makespan schedulingSpringer Science and Business Media LLC - Tập 183 - Trang 583-618 - 2020
Victor Verdugo, José Verschae, Andreas Wiese
The sum of squares (SoS) hierarchy gives an automatized technique to create a family of increasingly tight convex relaxations for binary programs. There are several problems for which a constant number of rounds of this hierarchy give integrality gaps matching the best known approximation algorithms. For many other problems, however, ad-hoc techniques give better approximation ratios than SoS in t...... hiện toàn bộ
A combined conjugate-gradient quasi-Newton minimization algorithmSpringer Science and Business Media LLC - Tập 15 - Trang 200-210 - 1978
A. G. Buckley
Although quasi-Newton algorithms generally converge in fewer iterations than conjugate gradient algorithms, they have the disadvantage of requiring substantially more storage. An algorithm will be described which uses an intermediate (and variable) amount of storage and which demonstrates convergence which is also intermediate, that is, generally better than that observed for conjugate gradient al...... hiện toàn bộ
Some upper and lower bounds on PSD-rankSpringer Science and Business Media LLC - Tập 162 - Trang 495-521 - 2016
Troy Lee, Zhaohui Wei, Ronald de Wolf
Positive semidefinite rank (PSD-rank) is a relatively new complexity measure on matrices, with applications to combinatorial optimization and communication complexity. We first study several basic properties of PSD-rank, and then develop new techniques for showing lower bounds on the PSD-rank. All of these bounds are based on viewing a positive semidefinite factorization of a matrix M as a quantum...... hiện toàn bộ