Journal ArticleDOI
Intersection Cuts—A New Type of Cutting Planes for Integer Programming
TLDR
The paper gives a simple formula for finding the equation of the hyperplane, discusses some ways of strengthening the cut, proposes an algorithm, and gives a finiteness proof.Abstract:
This paper proposes a new class of cutting planes for integer programming. A typical member of the class is generated as follows. Let X be the feasible set, and x the optimal (noninteger) solution...read more
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Journal ArticleDOI
A lift-and-project cutting plane algorithm for mixed 0-1 programs
TL;DR: A cutting plane algorithm for mixed 0–1 programs based on a family of polyhedra which strengthen the usual LP relaxation and shows how to generate a facet of a polyhedron in this family which is most violated by the current fractional point.
Journal ArticleDOI
Computational study of a family of mixed-integer quadratic programming problems
TL;DR: A branch-and-cut algorithm to solve quadratic programming problems where there is an upper bound on the number of positive variables and the algorithm solves the largest real-life problems in a few minutes of run-time.
Journal ArticleDOI
Branch-and-bound algorithms
TL;DR: A description of recent research advances in the design of B&B algorithms is presented, particularly with regards to the search strategy, the branching strategy, and the pruning rules.
Book ChapterDOI
Algorithms and Software for Convex Mixed Integer Nonlinear Programs
TL;DR: This paper provides a survey of recent progress and software for solving convex Mixed Integer Nonlinear Programs (MINLP)s, where the objective and constraints are defined by convex functions and integrality restrictions are imposed on a subset of the decision variables.
Journal ArticleDOI
Mixed 0-1 Programming by Lift-and-Project in a Branch-and-Cut Framework
TL;DR: In this article, the authors investigate the computational issues that need to be addressed when incorporating general cutting planes for mixed 0-1 programs into a branch-and-cut framework The cuts they use are of the lift-andproject variety and are of an experimental nature and are settled by comparing alternatives on a set of test problems.