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In this paper, we adapt the control theoretic concept of dissipativity theory to provide a natural understanding of Nesterov's accelerated method.
Introduction to optimization
Polyak, B. T · 1987
Earlier work this paper cites.
System analysis via integral quadratic constraints
Megretski, A. and Rantzer, A · 1997
Earlier work this paper cites.
Introductory Lectures on Convex Optimization: A Basic Course
Nesterov, Y · 2003
Earlier work this paper cites.
Control Systems Handbook , chapter 41: Integral Quadratic Constraints
Megretski, A., Jönsson, U., Kao, C. Y., and Rantzer, A · 2010
Earlier work this paper cites.
Convex optimization: Algorithms and complexity
Bubeck, S · 2015
Earlier work this paper cites.
A geometric alternative to Nesterov’s accelerated gradient descent
Bubeck, S., Lee, Y., and Singh, M · 2015
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From averaging to acceleration, there is only a step-size
Flammarion, N. and Bach, F · 2015
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Stability analysis with dissipation inequalities and integral quadratic constraints
Seiler, P · 2015
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An optimal first order method based on optimal quadratic averaging
Drusvyatskiy, D., Fazel, M., and Roy, S · 2016
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Exponential decay rate conditions for uncertain linear systems using integral quadratic constraints
Hu, B. and Seiler, P · 2016
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Dissipative dynamical systems Part I: General theory
Willems, J.C
Cited in the paper.
Dissipative dynamical systems Part II: Linear systems with quadratic supply rates
Willems, J.C
Cited in the paper.
Analysis and design of optimization algorithms via integral quadratic constraints
Lessard, L., Recht, B., and Packard, A · 2016
Later among the works it cites.
A differential equation for modeling Nesterov’s accelerated gradient method: Theory and insights
Su, W., Boyd, S., and Candès, E · 2016
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A variational perspective on accelerated methods in optimization
Wibisono, A., Wilson, A., and Jordan, M · 2016
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A Lyapunov analysis of momentum methods in optimization
Wilson, A., Recht, B., and Jordan, M · 2016
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Analysis of optimization algorithms via integral quadratic constraints: Nonstrongly convex problems
Fazlyab, M., Ribeiro, A., Morari, M., and Preciado, V. M · 2017
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