A note on solving nonlinear optimization problems in variable precision

2018/12/09 by Serge Gratton, Philippe L. Toint, Gratton, S. +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #65K05 #90C26 #90C30 #Advanced Optimization Algorithms Research #B.2.3 #B.2.4 #F.2.1 #FOS: Computer and information sciences #FOS: Mathematics #G.1.6 #I.2.5 #Machine Learning (cs.LG) #Mathematical Software (cs.MS) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1812.03467

openalex publication_date 2018/12/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

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. Numerical experiments are presented indicating that the use of the considered method can bring substantial savings in objective function's and gradient's evaluation "energy costs" by efficiently exploiting multi-precision computations.

Citations

• Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations
• Training Deep Neural Networks with 8-bit Floating Point Numbers
• Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization
• Numerical optimization

Cited by

• Recursive Bound-Constrained AdaGrad with Applications to Multilevel and Domain Decomposition Minimization

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