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Issue: Tập 23, Số 3 (2026)
Section: Articles
DOI: 10.54607/hcmue.js.23.3.4918(2026)
Date Published: 31/03/2026
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How to Cite
Bùi, H. T., Le, L. T., Tran, B. D., & Pham, D. K. (2026). GRADIENT-BASED METHODS FOR NOISY QUADRATIC OPTIMIZATION. Ho Chi Minh City University of Education Journal of Science, 23(3). https://doi.org/10.54607/hcmue.js.23.3.4918(2026)

GRADIENT-BASED METHODS FOR NOISY QUADRATIC OPTIMIZATION

Bui Huynh Tram1, , Le Lam Thuan1, Tran Ba Dat2, Pham Duy Khanh1
1 Ho Chi Minh City University of Education, Vietnam
2 Rowan University, The United States of America

Main Article Content

Abstract

In this paper, we study the problem of minimizing a noisy multivariate quadratic function using an inexact gradient descent framework, where the gradients are approximated via central finite difference schemes. Two noise models are analyzed: (i) the quadratic matrix is known, with noise in the linear and constant terms; (ii) both the matrix and linear term are known, with noise only in the constant term. We derive explicit error bounds, establish convergence rates using Polyak’s estimates (Polyak, 1987), and determine iteration complexity for the iterations generated by inexact gradient descent method with fixed step size.

Keywords

noisy multivariate quadratic functions, derivative-free optimization, central finite difference scheme, inexact gradient descent method

Article Details

References

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