On the Computation of the Efficient Frontier in Advanced Sparse Portfolio Optimization

TL;DR

This paper introduces a new algorithm for efficiently computing the entire set of optimal sparse portfolio solutions in multi-objective optimization, overcoming limitations of classical methods.

Contribution

A novel gradient-based algorithm with specialized initialization that outperforms traditional scalarization and genetic algorithms in sparse portfolio optimization.

Findings

Proposed method is significantly more effective than classical scalarization.

Algorithm outperforms popular genetic algorithms in computational experiments.

Efficiently computes a comprehensive front of solutions in sparse multi-objective problems.

Abstract

In this work, we deal with the problem of computing a comprehensive front of efficient solutions in multi-objective portfolio optimization problems in presence of sparsity constraints. We start the discussion pointing out some weaknesses of the classical linear scalarization approach when applied to the considered class of problems. We are then motivated to propose a suitable algorithmic framework that is designed to overcome these limitations: the novel algorithm combines a gradient-based exploration-refinement strategy with a tailored initialization scheme based on memetic or multi-start descent procedures. Thorough computational experiments highlight how the proposed method is far superior to both linear scalarization and popular genetic algorithms.