A quadratic simplex algorithm for primal optimization over zero-one polytopes

A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	Discrete Applied Mathematics Jg. 347; S. 285 - 296
1. Verfasser:	Mallach, Sven
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Elsevier B.V 15.04.2024
Schlagworte:	Binary quadratic programming Linearly-constrained quadratic programming Simplex algorithm Simplex algorithm Linearly-constrained quadratic programming Binary quadratic programming
ISSN:	0166-218X, 1872-6771
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	A primal quadratic simplex algorithm tailored to the optimization over the vertices of a polytope is presented. Starting from a feasible vertex, it performs either strictly improving or admissible non-deteriorating steps in order to determine a locally optimum basic feasible solution in terms of the quadratic objective function. The algorithm so generalizes over local improvement methods for according applications, including in particular quadratic optimization problems whose feasible solutions correspond to vertices of a 0-1 polytope. Computational experiments for unconstrained binary quadratic programs, maximum cut, and the quadratic assignment problem serve as a proof of concept and underline the importance of a pivoting rule that is able to accept at least a restricted class of degenerate steps.
ISSN:	0166-218X 1872-6771
DOI:	10.1016/j.dam.2023.12.030