Alternating minimization methods for strongly convex optimization

Abstract We consider alternating minimization procedures for convex and non-convex optimization problems with the vector of variables divided into several blocks, each block being amenable respect to its while maintaining other blocks constant. In case two we prove a linear convergence rate an procedure under Polyak–Łojasiewicz (PL) condition, which can be seen as relaxation strong convexity assumption. Under assumption in many-blocks setting, provide accelerated depending on square root condition number opposed just non-accelerated method. also problem finding approximate non-negative solution system equations A ⁢ x = y {Ax=y} Kullback–Leibler (KL) divergence between Ax y .