@inproceedings{84614bbd-bbc2-4b24-857f-6ba4064342e9,
  abstract     = {{<p>We present a general technique for efficient computation of second order information for optimization functionals involving many variables of different nature, frequently appearing in modern applications. This technique relies on the bilinear Hessian, and while the main tools for this task have been published elsewhere, we here focus on the problem of how to organize the computations in the multi-argument situation, relying on so called cascade optimization and the chain rule for the bilinear Hessian. For concreteness, we demonstrate our approach by focusing on three concrete problems; phase retrieval, multidistance nano-holotomography and training of neural networks. In the experimental section we present results where the proposed technique significantly speeds up first order methods, and in particular we obtain faster training results than the Adamalgorithm when training the so called SIREN neural network.<sup>1</sup><sup>1</sup>Supported by Swedish Research Council (grant no.</p>}},
  author       = {{Carlsson, Marcus and Bacca, Jorge and Wendt, Herwig and Nikitin, Viktor}},
  booktitle    = {{2025 IEEE 10th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2025 - Proceedings}},
  isbn         = {{9798331526696}},
  keywords     = {{bilinear Hessian; Cascade optimization; fast optimization; second order methods; Wirtinger calculus}},
  language     = {{eng}},
  pages        = {{341--345}},
  publisher    = {{IEEE - Institute of Electrical and Electronics Engineers Inc.}},
  title        = {{Cascade Computation of Second Order Information for Efficient Optimization of Multi-Argument Objective Functionals}},
  url          = {{http://dx.doi.org/10.1109/CAMSAP66162.2025.11423868}},
  doi          = {{10.1109/CAMSAP66162.2025.11423868}},
  year         = {{2025}},
}