We introduce the Line Search A-Function (LSAF) technique that generalizes the Extended-Baum Welch technique in order to provide an effective optimization technique for a broader set of functions. We show how LSAF can be applied to functions of various probability density and distribution functions by demonstrating that these probability functions have an A-function. We also show that sparse representation problems (SR) that use l1 or combination of l1/l2 regularization norms can also be efficiently optimized through an A-function derived for their objective functions. We will demonstrate the efficiency of LSAF for SR problems through simulations by comparing it with Approximate Bayesian Compressive Sensing method that we recently applied to speech recognition. © 2011 IEEE.