Linear programming and l<sub>1</sub>-norm minimization problems with convolution constraints

Hill, R 2005, 'Linear programming and l<sub>1</sub>-norm minimization problems with convolution constraints', in E. Camacho and R. Tempo (ed.) Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC'05), Seville, Spain, 12-15 December 2005.


Document type: Conference Paper
Collection: Conference Papers

Title Linear programming and l1-norm minimization problems with convolution constraints
Author(s) Hill, R
Year 2005
Conference name 44th IEEE Conference on Decision and Control and European Control Conference
Conference location Seville, Spain
Conference dates 12-15 December 2005
Proceedings title Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference (ECC'05)
Editor(s) E. Camacho
R. Tempo
Publisher IEEE
Place of publication USA
Abstract We illustrate some recent results on exact solutions to discrete-time l1 norm minimization problems with convolution constraints. A fixed-point property for this class of problems is introduced. The convolution constraints can be interpreted as a dynamic system with initial conditions. We show by construction that optimal solutions with a rational Z-transform exist for any initial conditions satisfying the fixed-point property. Some fixed-point initial conditions satisfy a further stability property. If there exists a stable fixed point, then for any initial condition in some neighbourhood of the fixed point an optimal solution can be constructed having a rational Z-transform.
Subjects Calculus of Variations, Systems Theory and Control Theory
Keyword(s) minimisation problems
convolution constraints
Copyright notice © 2005 IEEE
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