Abstract
This paper introduces a hybrid joint-selective optimization (HJSO) framework for large-scale numerical problems in which a small subset of trainable quantities is of primary interest. We partition the full parameter vector into a high-dimensional remaining block and a low-dimensional block of parameters of interest (POIs), perform joint first-order optimization over the full parameter set, and then freeze the remaining variables while applying a reduced-space Levenberg-Marquardt (LM) refinement to the POIs. The method is designed for settings in which the POIs are low-dimensional but strongly influence the quality of the computed solution, while the full parameter space remains too large for full-space second-order methods. The framework is evaluated on three representative problems: a matrix eigenvalue problem, an inverse Bratu problem solved with a physics-informed neural network, and a 100-dimensional nonlinear Black-Scholes problem solved with the DeepBSDE method. In each test, HJSO reaches prescribed POI-error thresholds faster than the corresponding joint first-order baseline and improves the final POI accuracy for the reported solver configurations. The contribution is therefore not a universal optimizer, but a practical reduced-space strategy for problems with known low-dimensional parameters of interest and expensive high-dimensional training variables.
Keywords
Subject
Publication details
- Journal
- Not available
- Open access
- Green open access
Cite this article
APA 7
Shahab, M. L., Indahsari, G. A., Mukhlash, I., & Susanto, H. (2026). Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest. https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest
MLA 9
Shahab, Muhammad Luthfi, et al. "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest." https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest.
Chicago (author–date)
Shahab, Muhammad Luthfi, Gabriella Alfa Indahsari, Imam Mukhlash, and Hadi Susanto. 2026. "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest." https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest.
Harvard
Shahab, M. L., Indahsari, G. A., Mukhlash, I. and Susanto, H. (2026) 'Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest', Available at: https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest.
Vancouver
Shahab ML, Indahsari GA, Mukhlash I, Susanto H. Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest. https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest
IEEE
M. L. Shahab, G. A. Indahsari, I. Mukhlash, and H. Susanto, "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest," https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest.