Fast Approximation Algorithms for a Class of Non-convex QCQP Problems Using First-Order Methods

A number of important problems in engineering can be formulated as non-convex quadratically constrained quadratic programming (QCQP). The general QCQP problem is NP-Hard. In this paper, we consider a class of non-convex QCQP problems that are expressible as the maximization of the point-wise minimum...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 65; no. 13; pp. 3494 - 3509
Main Authors: Konar, Aritra, Sidiropoulos, Nicholas D.
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2017
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Approximation
Approximation algorithms
Array signal processing
Beamforming
Complexity
Complexity theory
convergence
first-order methods
massive multiple-input multiple-output (MIMO) communications
Multicast
multicasting
Nemirovski saddle point reformulation
Nesterov smoothing
Non-convex optimization
non-smooth optimization
Optimization
per-antenna power constraints
Quadratic programming
quadratically constrained quadratic programming (QCQP)
Signal processing algorithms
Signal to noise ratio
Tradeoffs
Transmitting antennas
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:A number of important problems in engineering can be formulated as non-convex quadratically constrained quadratic programming (QCQP). The general QCQP problem is NP-Hard. In this paper, we consider a class of non-convex QCQP problems that are expressible as the maximization of the point-wise minimum of homogeneous convex quadratics over a "simple" convex set. Existing approximation strategies for such problems are generally incapable of achieving favorable performance-complexity tradeoffs. They are either characterized by good performance but high complexity and lack of scalability, or low complexity but relatively inferior performance. This paper focuses on bridging this gap by developing high performance, low complexity successive non-smooth convex approximation algorithms for problems in this class. Exploiting the structure inherent in each subproblem, specialized first-order methods are used to efficiently compute solutions. Multicast beamforming is considered as an application example to showcase the effectiveness of the proposed algorithms, which achieve a very favorable performance-complexity tradeoff relative to the existing state of the art.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2690386