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

A1 Journal article (refereed)

Internal Authors/Editors

Publication Details

List of Authors: Jan Kronqvist, Andreas Lundell, Tapio Westerlund
Publication year: 2016
Journal: Journal of Global Optimization
Volume number: 64
Issue number: 2
Start page: 249
End page: 272
eISSN: 1573-2916


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.

Last updated on 2019-17-06 at 04:28