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Linear Programming and l1-Norm Minimization Problems with Convolution Constraints

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1 Author(s)
Hill, R.D. ; Wackett Centre for Aerospace Design Technology, RMIT University, Melbourne, 3001, Australia.

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.

Published in:

Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on

Date of Conference:

12-15 Dec. 2005