[
    {
        "id": "osp-21790",
        "type": "article-journal",
        "title": "Hybrid Joint-Selective Optimization: Reduced-Space Levenberg-Marquardt Refinement of Low-Dimensional Parameters of Interest",
        "author": [
            {
                "family": "Shahab",
                "given": "Muhammad Luthfi"
            },
            {
                "family": "Indahsari",
                "given": "Gabriella Alfa"
            },
            {
                "family": "Mukhlash",
                "given": "Imam"
            },
            {
                "family": "Susanto",
                "given": "Hadi"
            }
        ],
        "URL": "https://omanscience.com/en/articles/hybrid-joint-selective-optimization-reduced-space-levenberg-marquardt-refinement-of-low-dimensional-parameters-of-interest",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "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."
    }
]