Eigendecomposition-based reformulations for convex MINLP in the SHOT solver

Jan Kronqvist*, Andreas Lundell

*Corresponding author for this work

Research output: Chapter in Book/Conference proceedingConference contributionScientific


In this extended abstract, we describe how the SHOT solver utilizes
eigendecomposition to perform a lifted reformulation for convex mixed-integer problems with non-separable quadratic expressions. An eigenvalue decomposition is first performed on the non-diagonal matrices defining quadratic expressions in the problem, and is used for transforming the quadratic expressions into convex additively separable constraints. The resulting additively separable constraints are then further lifted into a form where SHOT generates polyhedral outer approximations of convex quadratic univariate functions. The reformulations have been integrated into SHOT’s automatic problem reformulation functionality.
Original languageEnglish
Title of host publication Journal of Global Optimization
Subtitle of host publicationSpecial Issue on Global Optimization: HUGO
Number of pages4
Publication statusPublished - Sept 2022
MoE publication typeB3 Non-refereed article in conference proceedings
EventHungarian Global Optimization Workshop HUGO 2022 - Szeged, Hungary
Duration: 5 Sept 20228 Sept 2022

Publication series

Name Journal of Global Optimization
ISSN (Print)0925-5001
ISSN (Electronic)1573-2916


ConferenceHungarian Global Optimization Workshop HUGO 2022
Abbreviated titleHUGO


  • Mixed-integer nonlinear programming (MINLP)
  • eigendecomposition
  • Supporting hyperplane optimization toolkit (SHOT)
  • lifting reformulations
  • convex mixed-integer programming


Dive into the research topics of 'Eigendecomposition-based reformulations for convex MINLP in the SHOT solver'. Together they form a unique fingerprint.

Cite this