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DOI: 10.23952/cot.2025.17
Received January 16, 2024; Accepted April 20, 2024; Published online January 11, 2024
Abstract. The penalty function method has been widely used in many constrained optimization problems. However, a companion of such method is the ill-conditioning problem in the corresponding Hessian matrix. In this paper, a thorough investigation is provided to address this ill-conditioning problem. Our study reveals that this ill-conditioning is mathematically tractable. Furthermore, the resulting ill-conditioned system can be converted into a well-conditioned one. Consequently, this ill-conditioning problem can be overcome. Some theoretical results will be also provided. Our preliminary numerical tests have confirmed our findings.
How to Cite this Article:
L.Z. Liao, L. Hou, The ill-conditioning issue in the penalty function method, Commun. Optim. Theory 2025 (2025) 17.