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This short note considers an efficient variant of the trust-region algorithm with dynamic accuracy proposed Carter (1993) and Conn, Gould and Toint (2000) as a tool for very high-performance computing, an area where it is critical to allow multi-precision computations for keeping the energy dissipation under control.
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LANCELOT
A. R. Conn, N. I. M. Gould, and Ph. L. Toint · 1992
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Numerical experience with a class of algorithms for nonlinear optimization using inexact function and gradient information
R. G. Carter · 1993
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Performance of a multifrontal scheme for partially separable optimization
A. R. Conn, N. I. M. Gould, M. Lescrenier, and Ph. L. Toint · 1994
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A method of trust region type for minimizing noisy functions
C. Elster and A. Neumaier · 1997
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Numerical Optimization
J. Nocedal and S. J. Wright · 1999
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Trust-Region Methods
A. R. Conn, N. I. M. Gould, and Ph. L. Toint · 2000
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Accelerating scientific computations with mixed precision algorithms
M. Baboulin, A. Buttari, J. Dongarra, J. Kurzak, J. Langou, P. Luszczek, and S. Tomov · 2009
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Energy-efficient floating-point unit design
S. Galal and M. Horowitz · 2011
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A Levenberg-Marquardt method for large nonlinear least-squares problems with dynamic accuracy in functions and gradients
S. Bellavia, S. Gratton, and E. Riccietti · 2018
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S. Bellavia, G. Gurioli, and B. Morini · 2018
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S. Bellavia, G. Gurioli, B. Morini, and Ph. L. Toint · 2018
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A subsampling line-search method with second-order results
E. Bergou, Y. Diouane, V. Kungurtsev, and C. W. Royer · 2018
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Convergence rate analysis of a stochastic trust region method via supermartingales
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