New bounds for nonconvex quadratically constrained quadratic programming

In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of bounds for QCQPs, quadratic and cubic bounds. We use affine functions as Lagrange multipliers for quadratic bounds. We demonstrate that most semidefinite relaxations can be...

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Bibliographic Details
Published in:Journal of global optimization Vol. 85; no. 3; pp. 595 - 613
Main Author: Zamani, Moslem
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2023
Springer
Springer Nature B.V
Subjects:
Computer Science
Euclidean space
Lagrange multiplier
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Quadratic equations
Quadratic programming
Real Functions
Quadratically constrained quadratic programming
Reformulation-linearization technique
Semidefinite relaxation
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:In this paper, we study some bounds for nonconvex quadratically constrained quadratic programs (QCQPs). We propose two types of bounds for QCQPs, quadratic and cubic bounds. We use affine functions as Lagrange multipliers for quadratic bounds. We demonstrate that most semidefinite relaxations can be obtained as the dual of a quadratic bound. In addition, we study bounds obtained by changing the ground set. For cubic bounds, in addition to affine multipliers we employ quadratic functions. We provide a comparison between the proposed cubic bound and typical bounds for standard quadratic programs. Moreover, we report comparison results of some quadratic and cubic bounds.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-022-01224-1