Difference Between Iteratively Reweighted Least Squares (IRLS) and Sequential Quadratic Programming?
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.