Alternating direction methods for non convex optimization with applications to second-order least-squares and risk parity portfolio selection

In this paper we mainly focus on optimization of sums of squares of quadratic functions, which we refer to as second-order least-squares problems, subject to convex constraints. Our motivation arises from applications in risk parity portfolio selection. We generalize the setting further by considering a class of nonlinear, non convex functions which admit a (non … Read more

Least-squares approach to risk parity in portfolio selection

The risk parity optimization problem aims to find such portfolios for which the contributions of risk from all assets are equally weighted. Portfolios constructed using risk parity approach are a compromise between two well-known diversification techniques: minimum variance optimization approach and the equal weighting approach. In this paper, we discuss the problem of finding portfolios … Read more


We propose new versions of accelerated first order methods for convex composite optimization, where the prox parameter is allowed to increase from one iteration to the next. In particular we show that a full backtracking strategy can be used within the FISTA \cite{Beck-Teboulle-2009} and FALM algorithms \cite{Goldfarb-Ma-Scheinberg-2010} while preserving their worst-case iteration complexities of $O(\sqrt{L(f)/\epsilon})$. … Read more