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- Computational convex analysis using parametric quadratic...
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Computational convex analysis using parametric quadratic programming Jakee, Khan Md. Kamall
Abstract
The class of piecewise linear-quadratic (PLQ) functions is a very important class of functions in convex analysis since the result of most convex operators applied to a PLQ function is a PLQ function. Although there exists a wide range of algorithms for univariate PLQ functions, recent work has focused on extending these algorithms to PLQ functions with more than one variable. First, we recall a proof in [Convexity, Convergence and Feedback in Optimal Control, Phd thesis, R. Goebel, 2000] that PLQ functions are closed under partial conjugate computation. Then we use recent results on parametric quadratic programming (pQP) to compute the inf-projection of any multivariate convex PLQ function. We implemented the algorithm for bivariate PLQ functions, and modi ed it to compute conjugates. We provide a complete space and time worst-case complexity analysis and show that for bivariate functions, the algorithm matches the performance of [Computing the Conjugate of Convex Piecewise Linear-Quadratic Bivariate Functions, Bryan Gardiner and Yves Lucet, Mathematical Programming Series B, 2011] while being easier to extend to higher dimensions.
Item Metadata
Title |
Computational convex analysis using parametric quadratic programming
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
2013
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Description |
The class of piecewise linear-quadratic (PLQ) functions is a very important
class of functions in convex analysis since the result of most convex
operators applied to a PLQ function is a PLQ function. Although there exists
a wide range of algorithms for univariate PLQ functions, recent work has
focused on extending these algorithms to PLQ functions with more than one
variable. First, we recall a proof in [Convexity, Convergence and Feedback
in Optimal Control, Phd thesis, R. Goebel, 2000] that PLQ functions are
closed under partial conjugate computation. Then we use recent results on
parametric quadratic programming (pQP) to compute the inf-projection of
any multivariate convex PLQ function. We implemented the algorithm for
bivariate PLQ functions, and modi ed it to compute conjugates. We provide
a complete space and time worst-case complexity analysis and show that for
bivariate functions, the algorithm matches the performance of [Computing
the Conjugate of Convex Piecewise Linear-Quadratic Bivariate Functions,
Bryan Gardiner and Yves Lucet, Mathematical Programming Series B, 2011]
while being easier to extend to higher dimensions.
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Genre | |
Type | |
Language |
eng
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Date Available |
2013-10-01
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0074301
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Graduation Date |
2013-11
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Campus | |
Scholarly Level |
Graduate
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International