Volume 55, Number 1, January-February 2021
|Page(s)||247 - 260|
|Published online||15 March 2021|
On the minimum-norm solution of convex quadratic programming
Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
2 Department of Mathematics, Faculty of Science, University of Bojnord, Bojnord, Iran
3 Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Accepted: 24 January 2021
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.
Mathematics Subject Classification: 90C05 / 90C30 / 15A39
Key words: Solution set of convex problems / minimum-norm solution of convex quadratic programs / Newton’s method / theorems of alternative
© EDP Sciences, ROADEF, SMAI 2021
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