Abstract
In this paper, we propose a parallel algorithm for a fund of fund (FOF) optimization model. Based on the structure of objective function, we create an augmented Lagrangian function and separate the quadratic term from the nonlinear term by the alternate direction multiplier method (ADMM), which creates two new subproblems that are much easier to be computed. To accelerate the convergence speed of the proposed algorithm, we use an adaptive step size method to adjust the step parameter according to the residual of the dual problem at every iterate. We show the parallelization of the proposed algorithm and implement it on CUDA with block storage for the structured matrix, which is shown to be up to two orders of magnitude faster than the CPU implementation on large-scale problems.
Highlights
Fund of funds (FOF) has become a hot topic during the past several years
The parallel variable distribution (PVD) method is suitable for parallelization but needs to solve a difficult convex subproblem when applied to FOF optimization model, which makes it hard to be extended to large-scale problems
The main contribution of this paper is to propose a parallel algorithm general enough to characterize most of the existing specific FOF optimization models
Summary
Fund of funds (FOF) has become a hot topic during the past several years. As a mutual fund scheme, FOF uses other funds as investment targets and achieve the purpose of indirectly holding securities such as stocks and bonds [1]. The PVD method is suitable for parallelization but needs to solve a difficult convex subproblem when applied to FOF optimization model, which makes it hard to be extended to large-scale problems. In 1977, Glowinski and Marrocco [18] proposed the alternating direction method of multiplies (ADMM) based on the decomposition It is widely used in large-scale nonlinear optimization problems thanks to the advantage of being extended to parallel and distributed systems. This is followed by implementation details of the proposed parallel approach in Section 5,where we present the efficiency of the proposed approach compared with some of the best performing methods, as well as the acceleration effect of the parallel approach.
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