Saeed Ketabchi, Hossein Moosaei, and Milan Hladík. On the minimum-norm solution of convex quadratic programming. RAIRO-Oper. Res., 55(1):247–260, 2021.
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We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton’s method to solve this problem. Numerical results show that the proposed method is efficient.
@article{KetMoo2021a,
author = "Saeed Ketabchi and Hossein Moosaei and Milan Hlad\'{\i}k",
title = "On the minimum-norm solution of convex quadratic programming",
journal = "RAIRO-Oper. Res.",
fjournal = "RAIRO - Operations Research",
volume = "55",
number = "1",
pages = "247-260",
year = "2021",
doi = "10.1051/ro/2021011",
issn = "0399-0559",
bib2html_dl_html = "https://doi.org/10.1051/ro/2021011",
bib2html_dl_pdf = "https://doi.org/10.1051/ro/2021011",
abstract = "We discuss some basic concepts and present a numerical procedure for finding the minimum-norm solution of convex quadratic programs (QPs) subject to linear equality and inequality constraints. Our approach is based on a theorem of alternatives and on a convenient characterization of the solution set of convex QPs. We show that this problem can be reduced to a simple constrained minimization problem with a once-differentiable convex objective function. We use finite termination of an appropriate Newton’s method to solve this problem. Numerical results show that the proposed method is efficient.",
keywords = "Solution set of convex problems; Minimum-norm solution of convex quadratic programs; Newton’s method; Theorems of alternative",
}
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