Karl Welzel

Preprints

1. Cartis, C., Jerad, S., and Welzel, K. (2025). On Global Rates for Regularization Methods based on Secant Derivative Approximations. [arXiv]
   [BibTeX]

   @misc{2025_CartisJeradWelzel_Secantregularization_2509-07580,
     archiveprefix = {arXiv},
     eprint = {2509.07580},
     arxiv = {arXiv:2509.07580},
     primaryclass = {math.OC},
     year = {2025},
     author = {Cartis, Coralia and Jerad, Sadok and Welzel, Karl},
     title = {On Global Rates for Regularization Methods based on Secant Derivative Approximations},
     date = {2025-09-09}
   }

2. Welzel, K., Liu, Y., Hauser, R. A., and Cartis, C. (2025). Local Convergence of Adaptively Regularized Tensor Methods. [arXiv]
   [BibTeX]

   @misc{2025_WelzelLiuHauserCartis_Adaptivetensorconvergence_2510-25643,
     archiveprefix = {arXiv},
     eprint = {2510.25643},
     arxiv = {arXiv:2510.25643},
     primaryclass = {math.OC},
     year = {2025},
     author = {Welzel, Karl and Liu, Yang and Hauser, Raphael A. and Cartis, Coralia},
     title = {Local Convergence of Adaptively Regularized Tensor Methods},
     date = {2025-10-29}
   }

Full articles

1. Cartis, C., Hauser, R., Liu, Y., Welzel, K., and Zhu, W. (2026). Efficient Implementation of Third-order Tensor Methods with Adaptive Regularization for Unconstrained Optimization. Mathematical Programming Computation. DOI: 10.1007/s12532-026-00313-6 [arXiv]
   [BibTeX]

   @article{2024_CartisEtAl_TensormethodsRegularization_2501-00404,
     year = {2026},
     journal = {Mathematical Programming Computation},
     date = {2026-03-24},
     doi = {10.1007/s12532-026-00313-6},
     archiveprefix = {arXiv},
     eprint = {2501.00404},
     arxiv = {arXiv:2501.00404},
     primaryclass = {math.OC},
     author = {Cartis, Coralia and Hauser, Raphael and Liu, Yang and Welzel, Karl and Zhu, Wenqi},
     title = {Efficient Implementation of Third-order Tensor Methods with Adaptive Regularization for Unconstrained Optimization}
   }

2. Welzel, K., and Hauser, R. A. (2024). Approximating Higher-Order Derivative Tensors Using Secant Updates. SIAM Journal on Optimization, 34(1), 893–917. DOI: 10.1137/23m1549687 [arXiv]
   [BibTeX]

   @article{2023_WelzelHauser_Higherordersecant_2301-11678,
     year = {2024},
     journal = {SIAM Journal on Optimization},
     volume = {34},
     number = {1},
     pages = {893--917},
     doi = {10.1137/23m1549687},
     archiveprefix = {arXiv},
     eprint = {2301.11678},
     arxiv = {arXiv:2301.11678},
     primaryclass = {math.OC},
     author = {Welzel, Karl and Hauser, Raphael A.},
     title = {Approximating Higher-Order Derivative Tensors Using Secant Updates}
   }