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integer hull

Small Chvatal Rank

Published: 2007/07/20
  • Tristram Bogart
  • Rekha R. Thomas
  • Categories Cutting Plane Approaches, Polyhedra Tags cutting planes, integer hull, polyhedron, polytope

    We introduce a new measure of complexity of integer hulls of rational polyhedra called the small Chvatal rank (SCR). The SCR of an integer matrix A is the number of rounds of a Hilbert basis procedure needed to generate all normals of a sufficient set of inequalities to cut out the integer hulls of all … Read more

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    Keywords

    alternating direction method of multipliers approximation algorithms augmented lagrangian method bilevel optimization Branch-and-Bound branch-and-cut chance constraints column generation combinatorial optimization complexity conic optimization convex optimization cutting planes decomposition derivative-free optimization distributionally robust optimization duality dynamic programming first-order methods global convergence global optimization heuristics integer programming interior point methods large-scale optimization linear programming machine learning mixed-integer linear programming mixed-integer nonlinear programming mixed-integer programming multiobjective optimization nonconvex optimization nonlinear optimization nonlinear programming nonsmooth optimization optimal control optimization proximal point algorithm quadratic programming robust optimization semidefinite programming stochastic optimization stochastic programming trust-region methods unconstrained optimization

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