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Part of my work is concerned with applications in Sparse Bayesian Learning and therefore I occasionally stumble over interesting papers in the field of compressed sensing.

I recently read Iteratively Reweighted Algorithms for Compressive Sensing by Rick Chartrand and Wotao Yin (Available also on DocDroid).

The paper describes how using $ {L}_{p} $ -norms with $ p < 1 $ can be used to recover signals with fewer measurements than with the LASSO ($ {L}_{1} $ Regularization).
There is even a Wikipedia entry on Iteratively Reweighted Least Squares (IRLS).

However, I can't wrap my head around the difference between IRLS and Sequential Quadratic Programming (SQP). Is there any difference? The papers I have found on IRLS never mention SQP..

Many thanks in advance!

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SQP is a method for solving smooth (objective and constraint functions are at least twice differentiable) constrained nonlinear optimization problems. It solves a series of quadratic programming problems to converge to a solution to the Karush-Kuhn-Tucker conditions for the constrained optimization problem.

IRLS is a method for solving unconstrained minimization problems by solving a sequence of least squares problems which are obtained from the original problem by a rescaling at each iteration.

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