Relevant bibliographies by topics / Vector hessian

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Vector hessian'

Author: Grafiati
Published: 5 June 2025
Last updated: 1 August 2025

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Journal articles on the topic "Vector hessian"

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Ek, David, and Anders Forsgren. "Exact linesearch limited-memory quasi-Newton methods for minimizing a quadratic function." Computational Optimization and Applications 79, no. 3 (2021): 789–816. http://dx.doi.org/10.1007/s10589-021-00277-4.

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AbstractThe main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel to those of the BFGS method, or equivalently, to those of the method of preconditioned conjugate gradients. In the setting of reduced Hessians, the class provides a dynamical framework for the construction of limited-memory quasi-Newton methods. These methods attain finite termination on quadratic optimization problems in exact arithmetic. We show p
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Ito, Shin-ichi, Takeru Matsuda, and Yuto Miyatake. "Adjoint-based exact Hessian computation." BIT Numerical Mathematics 61, no. 2 (2021): 503–22. http://dx.doi.org/10.1007/s10543-020-00833-0.

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AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the H
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Tsuboi, Yuta, Yuya Unno, Hisashi Kashima, and Naoaki Okazaki. "Fast Newton-CG Method for Batch Learning of Conditional Random Fields." Proceedings of the AAAI Conference on Artificial Intelligence 25, no. 1 (2011): 489–94. http://dx.doi.org/10.1609/aaai.v25i1.7894.

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We propose a fast batch learning method for linear-chain Conditional Random Fields (CRFs) based on Newton-CG methods. Newton-CG methods are a variant of Newton method for high-dimensional problems. They only require the Hessian-vector products instead of the full Hessian matrices. To speed up Newton-CG methods for the CRF learning, we derive a novel dynamic programming procedure for the Hessian-vector products of the CRF objective function. The proposed procedure can reuse the byproducts of the time-consuming gradient computation for the Hessian-vector products to drastically reduce the total
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Luo, Zhijian, and Yuntao Qian. "Stochastic sub-sampled Newton method with variance reduction." International Journal of Wavelets, Multiresolution and Information Processing 17, no. 06 (2019): 1950041. http://dx.doi.org/10.1142/s0219691319500413.

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Stochastic optimization on large-scale machine learning problems has been developed dramatically since stochastic gradient methods with variance reduction technique were introduced. Several stochastic second-order methods, which approximate curvature information by the Hessian in stochastic setting, have been proposed for improvements. In this paper, we introduce a Stochastic Sub-Sampled Newton method with Variance Reduction (S2NMVR), which incorporates the sub-sampled Newton method and stochastic variance-reduced gradient. For many machine learning problems, the linear time Hessian-vector pro
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Yong, Peng, Romain Brossier, and Ludovic Métivier. "Parsimonious truncated Newton method for time-domain full-waveform inversion based on the Fourier-domain full-scattered-field approximation." GEOPHYSICS 87, no. 1 (2021): R123—R146. http://dx.doi.org/10.1190/geo2021-0164.1.

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To exploit Hessian information in full-waveform inversion (FWI), the matrix-free truncated Newton method can be used. In such a method, Hessian-vector product computation is one of the major concerns due to the huge memory requirements and demanding computational cost. Using the adjoint-state method, the Hessian-vector product can be estimated by zero-lag crosscorrelation of the first-/second-order incident wavefields and the second-/first-order adjoint wavefields. Different from the implementation in frequency-domain FWI, Hessian-vector product construction in the time domain becomes much mor
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López-Marcos, M. A., J. M. Sanz-Serna, and Robert D. Skeel. "Explicit Symplectic Integrators Using Hessian--Vector Products." SIAM Journal on Scientific Computing 18, no. 1 (1997): 223–38. http://dx.doi.org/10.1137/s1064827595288085.

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Cong, Yulai, Miaoyun Zhao, Jianqiao Li, Junya Chen, and Lawrence Carin. "GO Hessian for Expectation-Based Objectives." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 13 (2021): 12060–68. http://dx.doi.org/10.1609/aaai.v35i13.17432.

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An unbiased low-variance gradient estimator, termed GO gradient, was proposed recently for expectation-based objectives E_q_γ(y) [f(y)], where the random variable (RV) y may be drawn from a stochastic computation graph (SCG) with continuous (non-reparameterizable) internal nodes and continuous/discrete leaves. Based on the GO gradient, we present for E_q_γ(y) [f(y)] an unbiased low-variance Hessian estimator, named GO Hessian, which contains the deterministic Hessian as a special case. Considering practical implementation, we reveal that the GO Hessian in expectation obeys the chain rule and i
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Liu, Weifeng, Lianbo Zhang, Dapeng Tao, and Jun Cheng. "Support vector machine active learning by Hessian regularization." Journal of Visual Communication and Image Representation 49 (November 2017): 47–56. http://dx.doi.org/10.1016/j.jvcir.2017.08.001.

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Jiang, Ting, and XiaoJian Zhou. "Gradient/Hessian-enhanced least square support vector regression." Information Processing Letters 134 (June 2018): 1–8. http://dx.doi.org/10.1016/j.ipl.2018.01.014.

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Trudinger, Neil S. "On Hessian Measures for Non-Commuting Vector Fields." Pure and Applied Mathematics Quarterly 2, no. 1 (2006): 147–61. http://dx.doi.org/10.4310/pamq.2006.v2.n1.a6.

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Dissertations / Theses on the topic "Vector hessian"

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Watson, Francis Maurice. "Better imaging for landmine detection : an exploration of 3D full-wave inversion for ground-penetrating radar." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/better-imaging-for-landmine-detection-an-exploration-of-3d-fullwave-inversion-for-groundpenetrating-radar(720bab5f-03a7-4531-9a56-7121609b3ef0).html.

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Humanitarian clearance of minefields is most often carried out by hand, conventionally using a a metal detector and a probe. Detection is a very slow process, as every piece of detected metal must treated as if it were a landmine and carefully probed and excavated, while many of them are not. The process can be safely sped up by use of Ground-Penetrating Radar (GPR) to image the subsurface, to verify metal detection results and safely ignore any objects which could not possibly be a landmine. In this thesis, we explore the possibility of using Full Wave Inversion (FWI) to improve GPR imaging f
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Song, Lili. "Modeling Hessian-Vector Products in Nonlinear Optimization: New Hessian-Free Methods." Doctoral thesis, 2022. http://hdl.handle.net/10316/98611.

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Tese no âmbito do Programa Inter-Universitário de Doutoramento em Matemática apresentada à Faculdade de Ciências e Tecnologia da Universidade de Coimbra.<br>In this dissertation, two approaches are proposed to calculate interpolation models for unconstrained smooth nonlinear optimization when Hessian-vector products are available. The main idea is to interpolate the objective function by a quadratic, using function evaluations on a set of points around the current one, and concurrently using the curvature information from products of the Hessian times appropriate vectors, possibly defined by t
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Book chapters on the topic "Vector hessian"

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Reiz, Severin, Tobias Neckel, and Hans-Joachim Bungartz. "Neural Nets with a Newton Conjugate Gradient Method on Multiple GPUs." In Parallel Processing and Applied Mathematics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-30442-2_11.

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AbstractTraining deep neural networks consumes increasing computational resource shares in many compute centers. Often, a brute force approach to obtain hyperparameter values is employed. Our goal is (1) to enhance this by enabling second-order optimization methods with fewer hyperparameters for large-scale neural networks and (2) to compare optimizers for specific tasks to suggest users the best one for their problem. We introduce a novel second-order optimization method that requires the effect of the Hessian on a vector only and avoids the huge cost of explicitly setting up the Hessian for
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Lin, Psang Dain. "Hessian Matrix of Boundary Variable Vector X̄i with Respect to System Variable Vector X̄sys." In Advanced Geometrical Optics. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2299-9_17.

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Lin, Psang Dain. "Hessian Matrices of Ray R̄i with Respect to Incoming Ray R̄i-1 and Boundary Variable Vector X̄i." In Advanced Geometrical Optics. Springer Singapore, 2016. http://dx.doi.org/10.1007/978-981-10-2299-9_16.

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Miguel García-Guzman, Jose, Néstor González-Cabrera, Luis Alberto Contreras-Aguilar, Jose Merced Lozano-García, and Alejandro Pizano-Martinez. "Analysis of Optimal Steady-State Operation of Power Systems with Embedded FACTS Devices: A Matlab-Based Flexible Approach." In Renewable Energy [Working Title]. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.93519.

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This book chapter presents a flexible approach to incorporate mathematical models of FACTS devices into the Power Flow (PF) and the Optimal Power Flow (OPF) analysis tools, as well as into the standard OPF Market-Clearing (OPF-MC) procedure. The proposed approach uses the Matlab Optimization Toolbox because it allows to easily: (a) implement a given optimization model, (b) include different objective functions using distinct equality and inequality constraints and (c) modify and reuse an optimization model that has been previously implemented. The conventional OPF model is the main core of the
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Conference papers on the topic "Vector hessian"

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Song, Caifeng, Weifeng Liu, and Yanjiang Wang. "Facial expression recognition based on Hessian regularized support vector machine." In the Fifth International Conference. ACM Press, 2013. http://dx.doi.org/10.1145/2499788.2499858.

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Nimura, Yukitaka, Takayuki Kitasaka, and Kensaku Mori. "Blood vessel segmentation using line-direction vector based on Hessian analysis." In SPIE Medical Imaging, edited by Benoit M. Dawant and David R. Haynor. SPIE, 2010. http://dx.doi.org/10.1117/12.844672.

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Wang, Y. Q., W. F. Chen, T. L. Yu, and Y. T. Zhang. "Hessian based image structure adaptive gradient vector flow for parametric active contours." In 2010 17th IEEE International Conference on Image Processing (ICIP 2010). IEEE, 2010. http://dx.doi.org/10.1109/icip.2010.5654358.

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Li, Weiling, and Xin Luo. "A Generalized-Momentum-Accelerated Hessian-Vector Algorithm for High-Dimensional and Sparse Data." In 2020 IEEE International Conference on Data Mining (ICDM). IEEE, 2020. http://dx.doi.org/10.1109/icdm50108.2020.00134.

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Cao, Weiguo, Marc J. Pomeroy, Yongfeng Gao, et al. "An Investigation for Colorectal Cancer Early Diagnosis Using Hessian Vector-based Texture Features." In 2021 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC). IEEE, 2021. http://dx.doi.org/10.1109/nss/mic44867.2021.9875916.

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Peng, Wensi, and Sivakumaran Nadarajah. "Truncated-Newton Method with Adjoint-based Hessian-vector Product for Aerodynamic Shape Optimization Problems." In AIAA Scitech 2020 Forum. American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-1293.

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Li, Weiling, Xin Luo, and MengChu Zhou. "A Generalized Nesterov-Accelerated Hessian-Vector-Based Latent Factor Analysis Model for QoS Prediction." In 2021 IEEE 14th International Conference on Cloud Computing (CLOUD). IEEE, 2021. http://dx.doi.org/10.1109/cloud53861.2021.00033.

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Kim, HeeChang, Georges Stamon, and Auguste Genovesio. "A method for discontinuous neurite reconstruction based on diffusion tensor, Hessian eigenvector, and diffused gradient vector fields." In 2011 18th IEEE International Conference on Image Processing (ICIP 2011). IEEE, 2011. http://dx.doi.org/10.1109/icip.2011.6115702.

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