2019/06/13 by Mayeli, Azita
#26B25 #65K05 #65K10 #90C26 #90C30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.1906.05608
In this paper, we introduce a class of nonsmooth nonconvex least square optimization problem using convex analysis tools and we propose to use the iterative minimization-majorization (MM) algorithm on a convex set with initializer away from the origin to find an optimal point for the optimization problem. For this, first we use an approach to construct a class of convex majorizers which approximate the value of non-convex cost function on a convex set. The convergence of the iterative algorithm is guaranteed when the initial point x(0) is away from the origin and the iterative points x(k) are obtained in a ball centred at x(k-1) with small radius. The algorithm converges to a stationary point of cost function when the surregators are strongly convex. For the class of our optimization problems, the proposed penalizer of the cost function is the difference of ℓ1-norm and the Moreau envelope of a convex function, and it is a generalization of GMC non-separable penalty function previously introduced by Ivan Selesnick in \citeIS17.