An approximation algorithm for indefinite mixed integer quadratic programming

In this paper, we give an algorithm that finds an ϵ -approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected...

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Bibliographic Details
Published in:Mathematical programming Vol. 201; no. 1-2; pp. 263 - 293
Main Author: Pia, Alberto Del
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023
Springer
Subjects:
Algorithms
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Theoretical
90C20
Mixed integer quadratic programming
Symmetric decomposition
90C11
90C26
90C59
Approximation algorithm
Simultaneous diagonalization
Polynomial time
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary:In this paper, we give an algorithm that finds an ϵ -approximate solution to a mixed integer quadratic programming (MIQP) problem. The algorithm runs in polynomial time if the rank of the quadratic function and the number of integer variables are fixed. The running time of the algorithm is expected unless P = NP. In order to design this algorithm we introduce the novel concepts of spherical form MIQP and of aligned vectors, and we provide a number of results of independent interest. In particular, we give a strongly polynomial algorithm to find a symmetric decomposition of a matrix, and show a related result on simultaneous diagonalization of matrices.
ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-022-01907-3