EURO 2025 Leeds
Abstract Submission

2640. An Approximate Subgradient Based Method to Solve Nonsmooth Optimization Problem Under Data Uncertainty with Application to Portfolio Selection

Invited abstract in session MC-50: Splitting algorithms, stream Variational analysis, equilibria and nonsmooth optimization.

Monday, 12:30-14:00
Room: Parkinson B11

Authors (first author is the speaker)

1. Priyanka Roy
Mathematics division, School of Advanced Sciences and Languages, VIT Bhopal University

Abstract

This study introduces an approximate subgradient-based method to address nonsmooth optimization problems under data uncertainty. Traditional optimization techniques often struggle with nonsmoothness and uncertainty, particularly in real-world applications. Here we consider the nonsmooth objective functions whose coefficients are varying within a closed interval under data uncertainty. The proposed method integrates advanced concepts from interval analysis and nonsmooth optimization to deliver robust solutions under uncertainty. This method utilizes the generalized Hukuhara subdifferential concept with epsilon approximation to compute an approximate solution within tolerance level that can handle nonsmoothness with interval uncertainty. Based on theoretical analysis, we proposed the approximate gH-subgradient method to solve nonsmooth interval-valued optimization along with detailed convergence analysis and suitable numerical illustration. As an application, we applied the proposed algorithm to portfolio selection models. The approach minimizes interval-valued risk with uncertain returns and covariances. It generates portfolios that stabilize risk across best- and worst-case scenarios, offering pragmatic solutions for financial decision-making under uncertainty. A numerical case study with three assets illustrates the method’s efficacy, converging to portfolio weights that stabilize risk within tolerance bounds.

Keywords

Status: accepted

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