Robust and Sparse Portfolio: Optimization Models and Algorithms

Abstract

The robust and sparse portfolio selection problem is one of the most-popular and -frequently studied problems in the optimization and financial literature. By considering the uncertainty of the parameters, the goal is to construct a sparse portfolio with low volatility and decent returns, subject to other investment constraints. In this paper, we propose a new portfolio selection model, which considers the perturbation in the asset return matrix and the parameter uncertainty in the expected asset return. We define three types of stationary points of the penalty problem: the Karush–Kuhn–Tucker point, the strong Karush–Kuhn–Tucker point, and the partial minimizer. We analyze the relationship between these stationary points and the local/global minimizer of the penalty model under mild conditions. We design a penalty alternating-direction method to obtain the solutions. Compared with several existing portfolio models on seven real-world datasets, extensive numerical experiments demonstrate the robustness and effectiveness of our model in generating lower volatility.

Optimizing the Economic Order Quantity Using Fuzzy Theory and Machine Learning Applied to a Pharmaceutical Framework

“…To cover this gap and expanding upon prior research, which focuses on a single commodity with one supplier and one buyer [2,29], we propose and develop a model that incorporates novel elements such as pentagonal fuzzy number (PFN) arithmetic for cost and consumption assessment, in combination with Kuhn-Tucker optimization techniques [30]. This model aligns with advanced optimization and algorithms, as discussed in [31], with a focus on the importance of robust and adaptable optimization strategies in complex inventory systems. The analysis of complex data patterns and the formulation of uncertainty can benefit from the application of advanced statistical models, as discussed in [32].…”