The extended supporting hyperplane algorithm for convex mixed-integer nonlinear programming

A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and...

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Bibliographic Details
Published in:Journal of global optimization Vol. 64; no. 2; pp. 249 - 272
Main Authors: Kronqvist, Jan, Lundell, Andreas, Westerlund, Tapio
Format: Journal Article
Language:English
Published: New York Springer US 01.02.2016
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Computer Science
Hyperplanes
Integer programming
Libraries
Linear programming
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear programming
Operations Research/Decision Theory
Optimization
Performance evaluation
Quadratic programming
Real Functions
Searching
Shot
Solvers
Studies
Variables
Extended cutting plane (ECP) algorithm
Convex MINLP
Supporting hyperplanes
Cutting planes
Supporting hyperplane optimization toolkit (SHOT)
Extended supporting hyperplane (ESH) algorithm
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:A new deterministic algorithm for solving convex mixed-integer nonlinear programming (MINLP) problems is presented in this paper: The extended supporting hyperplane (ESH) algorithm uses supporting hyperplanes to generate a tight overestimated polyhedral set of the feasible set defined by linear and nonlinear constraints. A sequence of linear or quadratic integer-relaxed subproblems are first solved to rapidly generate a tight linear relaxation of the original MINLP problem. After an initial overestimated set has been obtained the algorithm solves a sequence of mixed-integer linear programming or mixed-integer quadratic programming subproblems and refines the overestimated set by generating more supporting hyperplanes in each iteration. Compared to the extended cutting plane algorithm ESH generates a tighter overestimated set and unlike outer approximation the generation point for the supporting hyperplanes is found by a simple line search procedure. In this paper it is proven that the ESH algorithm converges to a global optimum for convex MINLP problems. The ESH algorithm is implemented as the supporting hyperplane optimization toolkit (SHOT) solver, and an extensive numerical comparison of its performance against other state-of-the-art MINLP solvers is presented.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-015-0322-3