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...

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Bibliographic Details
Published in:Discrete Applied Mathematics Vol. 347; pp. 285 - 296
Main Author: Mallach, Sven
Format: Journal Article
Language:English
Published: Elsevier B.V 15.04.2024
Subjects:
Binary quadratic programming
Linearly-constrained quadratic programming
Simplex algorithm
Simplex algorithm
Linearly-constrained quadratic programming
Binary quadratic programming
ISSN:0166-218X, 1872-6771
Online Access:Get full text
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Summary: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