Penalty Alternating Direction Methods for Mixed-Integer Optimization: A New View on Feasibility Pumps

Journal article
(Original article)


Publication Details

Author(s): Geißler B, Morsi A, Schewe L, Schmidt M
Journal: SIAM Journal on Optimization
Publisher: Taylor & Francis
Publication year: 2017
Volume: 27
Journal issue: 3
Pages range: 1611-1636
ISSN: 1052-6234
Language: English


Abstract


Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only few works considering their theoretical properties. We show that feasibility pumps can be seen as alternating direction methods applied to special reformulations of the original problem, inheriting the convergence theory of these methods. Moreover, we propose a novel penalty framework that encompasses this alternating direction method, which allows us to refrain from random perturbations that are applied in standard versions of feasibility pumps in case of failure. We present a convergence theory for the new penalty based alternating direction method and compare the new variant of the feasibility pump with existing versions in an extensive numerical study for mixed-integer linear and nonlinear problems.



FAU Authors / FAU Editors

Geißler, Björn Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Morsi, Antonio Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schewe, Lars PD Dr.
Economics - Discrete Optimization - Mathematics (EDOM)
Schmidt, Martin Prof. Dr.
Juniorprofessur für Optimierung von Energiesystemen


How to cite

APA:
Geißler, B., Morsi, A., Schewe, L., & Schmidt, M. (2017). Penalty Alternating Direction Methods for Mixed-Integer Optimization: A New View on Feasibility Pumps. SIAM Journal on Optimization, 27(3), 1611-1636. https://dx.doi.org/10.1137/16M1069687

MLA:
Geißler, Björn, et al. "Penalty Alternating Direction Methods for Mixed-Integer Optimization: A New View on Feasibility Pumps." SIAM Journal on Optimization 27.3 (2017): 1611-1636.

BibTeX: 

Last updated on 2018-11-08 at 02:24