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

A1 Originalartikel i en vetenskaplig tidskrift (referentgranskad)


Interna författare/redaktörer


Publikationens författare: Jan Kronqvist, Andreas Lundell, Tapio Westerlund
Publiceringsår: 2016
Tidskrift: Journal of Global Optimization
Volym: 64
Nummer: 2
Artikelns första sida, sidnummer: 249
Artikelns sista sida, sidnummer: 272
eISSN: 1573-2916


Abstrakt

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.

Senast uppdaterad 2019-12-12 vid 02:47