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We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning.
Gradient methods for minimizing functionals
Polyak, B. T · 1963
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Error bounds and convergence analysis of feasible descent methods: a general approach
Luo, Z.-Q · 1993
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Numerical optimization
Nocedal, J · 2006
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Markov processes: characterization and convergence
Ethier, S. N · 2009
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Efficiency of coordinate descent methods on huge-scale optimization problems
Nesterov, Y · 2012
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Introductory lectures on convex optimization: A basic course
Nesterov, Y · 2013
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Gradient methods for convex minimization: better rates under weaker conditions
Zhang, H · 2013
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Linear convergence of variance-reduced stochastic gradient without strong convexity
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Linear convergence of first order methods for non-strongly convex optimization
Convex analysis
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Linear convergence of gradient and proximal-gradient methods under the polyak-łojasiewicz condition
Karimi, H · 2016
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A variational perspective on accelerated methods in optimization
Wibisono, A · 2016
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A lyapunov analysis of momentum methods in optimization
Wilson, A. C · 2016
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New analysis of linear convergence of gradient-type methods via unifying error bound conditions
Zhang, H · 2016
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Necoara, I · 2015
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