Convex optimization problems involving finite autocorrelation sequences

We discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in...

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Published in:Mathematical programming Vol. 93; no. 3; pp. 331 - 359
Main Authors: Alkire, Brien, Vandenberghe, Lieven
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.12.2002
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Convex analysis
Digital Object Identifier
Exact sciences and technology
Fourier transforms
Mathematical programming
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Semidefinite programming
Signal processing
System theory
Variables
Autocorrelation function
Filter
Kalman filter
Linear matrix inequality
Interior point method
Signal processing
Semi definite programming
System identification
Sampling
Convex programming
Constrained optimization
Mathematical programming
ISSN:0025-5610, 1436-4646
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Abstract We discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in a set of linear inequalities. They can also be cast as linear matrix inequalities via the Kalman-Yakubovich-Popov lemma. The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interior-point methods for semidefinite programming. However, it has an important drawback: to represent an autocorrelation sequence of length $n$, it requires the introduction of a large number ($n(n+1)/2$) of auxiliary variables. This results in a high computational cost when general-purpose semidefinite programming solvers are used. We present a more efficient implementation based on duality and on interior-point methods for convex problems with generalized linear inequalities.
AbstractList We discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in signal processing and communications, and we describe applications in filter design and system identification. Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in a set of linear inequalities. They can also be cast as linear matrix inequalities via the Kalman-Yakubovich-Popov lemma. The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interior-point methods for semidefinite programming. However, it has an important drawback: to represent an autocorrelation sequence of length $n$, it requires the introduction of a large number ($n(n+1)/2$) of auxiliary variables. This results in a high computational cost when general-purpose semidefinite programming solvers are used. We present a more efficient implementation based on duality and on interior-point methods for convex problems with generalized linear inequalities.
Author Vandenberghe, Lieven
Alkire, Brien
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Issue 3
Keywords Autocorrelation function
Filter
Kalman filter
Linear matrix inequality
Interior point method
Signal processing
Semi definite programming
System identification
Sampling
Convex programming
Constrained optimization
Mathematical programming
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Snippet We discuss convex optimization problems in which some of the variables are constrained to be finite autocorrelation sequences. Problems of this form arise in...
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SubjectTerms Algorithms
Applied sciences
Convex analysis
Digital Object Identifier
Exact sciences and technology
Fourier transforms
Mathematical programming
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Semidefinite programming
Signal processing
System theory
Variables
Title Convex optimization problems involving finite autocorrelation sequences
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