- Referenced in 465 articles
- problem will be considered with respect to relaxations, bounds, reductions and other algorithmic techniques...
- Referenced in 301 articles
- programming (SDP), or linear matrix inequality (LMI) relaxations of the GPM, whose associated monotone sequence...
- Referenced in 190 articles
- integer nonlinear problems that exhibit convex continuous relaxations, on which the experiments are carried...
- Referenced in 115 articles
- branch-and-bound algorithms using linear programming relaxations. Cutting planes or columns can be generated ... used to solve the relaxations. Moreover, ABACUS provides a variety of general algorithmic concepts...
- Referenced in 132 articles
- branch-and-bound algorithm with linear programming relaxations. It also provides automatic constraint classification, preprocessing...
- Referenced in 127 articles
- sequence of fractional solutions of the LP relaxation, until a feasible one is eventually found...
- Referenced in 72 articles
- optimality by intersecting semidefinite and polyhedral relaxations. We present a method for finding exact solutions ... solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part ... bounding procedure is solving the basic semidefinite relaxation of the Max-Cut problem, which...
- Referenced in 65 articles
- SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation ... sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial ... Waki et al. . The sparse SDP relaxation exploits a sparse structure of polynomials ... POPs when applying “a hierarchy of LMI relaxations of increasing dimensions” Lasserre . The efficiency...
- Referenced in 44 articles
- open source software library for calculating convex/concave relaxations of factorable functions as well as subgradients ... these relaxations. libMC has been succeeded by MC++. For the automatic generation of convex ... concave relaxations of a given factorable function, a recursive procedure is first employed to develop ... enclosures as well as convex and concave relaxations recursively for each of these intermediate variables...
- Referenced in 63 articles
- strategies are available for choosing the relaxation parameter and the stopping rule. The relaxation parameter...
- Referenced in 80 articles
- purpose, along with a variety of convex-relaxation algorithms for finding good solutions. We pursue...
- Referenced in 42 articles
- Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs The Goemans--Williamson ... need for solving an expensive semidefinite relaxation. In order to achieve better practical performance ... propose an alternative, rank-two relaxation and develop a specialized version of the Goemans--Williamson ... computer code based on the rank-two relaxation heuristics is compared with two state...
- Referenced in 66 articles
- Data analysis sometimes requires the relaxation of parametric assumptions in order to gain modeling flexibility...
- Referenced in 39 articles
- minimum cost flow problems that combines the RELAX code (see two papers by Bertsekas ... example long augmenting paths, for which the relaxation method has been known to be slow ... significantly deteriorate the performance of the relaxation method for the types of problems where...
- Referenced in 60 articles
- truss topology design, control systems engineering, and relaxations of combinatorial optimization problems. The current version...
- Referenced in 59 articles
- cutting plane method. Instead of solving every relaxed master problem to optimality...
- Referenced in 33 articles
- number of segments in the piecewise relaxation. Inspired by recent work ... introduce a formulation for the piecewise linear relaxation of bilinear functions with a logarithmic number ... formulation to the best-performing piecewise relaxations with a linear number of binary variables...
- Referenced in 32 articles
- Sparse Version of Full Semidefinite Programming Relaxation for Sensor Network Localization Problems SFSDP ... networks. SFSDP implements the semidefinite programming (SDP) relaxation proposed ... sparse version of the full semidefinite programming relaxation (FSDP) by Biswas...
- Referenced in 28 articles
- QUICKXPLAIN: preferred explanations and relaxations for over-constrained problems. Over-constrained problems can have ... failure, and an exponential number of relaxations, which restore the consistency. A user ... interactive application, however, desires explanations and relaxations containing the most important constraints. To address this ... need, we define preferred explanations and relaxations based on user preferences between constraints...
- Referenced in 25 articles
- RELAX-IV: A faster version of the RELAX code for solving minimum cost flow problems ... solution by means of a heuristic initialization. RELAX-IV is a minimum cost ﬂow code ... that combines the RELAX code of [BeT88a], [BeT88b] with an initialization based on a recently ... example long augmenting paths, for which the relaxation method has been known to be slow...