The maximum feasible subsystem problem and vertex-facet incidences of polyhedra
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The article was published on 2003-01-17 and is currently open access. It has received 40 citations till now. The article focuses on the topics: Vertex (geometry) & Polyhedron.read more
Citations
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A bounded-error approach to piecewise affine system identification
TL;DR: This paper proposes a three-stage procedure for parametric identification of piecewise affine autoregressive exogenous (PWARX) models and imposes that the identification error is bounded by a quantity /spl delta/.
Generating All Vertices of a Polyhedron is Hard
TL;DR: It is shown that generating all negative cycles of a weighted graph is a hard enumeration problem, in both the directed and undirected cases, implying that (directed) negative cycles cannot be generated in polynomial output time, unless P=NP.
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HySAT: An efficient proof engine for bounded model checking of hybrid systems
Martin Fränzle,Christian Herde +1 more
TL;DR: HySAT is presented, a bounded model checker for linear hybrid systems, incorporating a tight integration of a DPLL–based pseudo–Boolean SAT solver and a linear programming routine as core engine and it is demonstrated that those optimizations are crucial to the performance of the tool.
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Generating All Vertices of a Polyhedron Is Hard
TL;DR: In this paper, it was shown that given a family of negative cycles, it is an NP-complete problem to decide whether this family can be extended or there are no other negative cycles in the graph, implying that (directed) negative cycles cannot be generated in polynomial output time.
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Conflict analysis in mixed integer programming
TL;DR: This paper presents heuristics for branch-and-cut solvers to generate valid inequalities from the current infeasible subproblem and the associated branching information and generalizes SAT infeasibility analysis to mixed integer programming.
References
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Book
Integer and Combinatorial Optimization
TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
Book
Geometric Algorithms and Combinatorial Optimization
TL;DR: In this article, the Fulkerson Prize was won by the Mathematical Programming Society and the American Mathematical Society for proving polynomial time solvability of problems in convexity theory, geometry, and combinatorial optimization.