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Splitting Methods for Distributed Optimization and Control

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Forward-Backward Splitting for Optimal Transport Based Problems

Pascal Frossard, Guillermo Ortiz Jimenez, Mireille El Gheche, Hermina Petric Maretic, Effrosyni Simou

Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When the entropy regula ...

2020

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Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed deterministic optimization problems. These methods employ constant step-sizes and converge linearly to the exact ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

A Catalyst Framework for Minimax Optimization

Negar Kiyavash

We introduce a generic \emph{two-loop} scheme for smooth minimax optimization with strongly-convex-concave objectives. Our approach applies the accelerated proximal point framework (or Catalyst) to the associated \emph{dual problem} and takes full advantag ...

2020

Optimization algorithms and Monte Carlo sampling algorithms have provided the computational foundations for the rapid growth in applications of statistical machine learning in recent years. There is, however, limited theoretical understanding of the relati ...

PNAS2019

A Time Splitting Based Real-Time Iteration Scheme for Nonlinear MPC

Colin Neil Jones, Yuning Jiang

This paper proposes a parallelizable real-time algorithm for model predictive control (MPC). In contrast to existing distributed and parallel optimization algorithms for linear MPC such as dual decomposition or the alternating direction method of multiplie ...

IEEE2019

Very-High-Speed Miniaturized Permanent Magnet Motors: Design and Optimization

Yves Perriard, Guillaume Paul-André Burnand

This paper aims to present an optimization method for very-high-speed electrical machines based on multiphysical analytical models. Analytical models allow a fast design but have to be robust and reliable. The set of models presented is very complete and c ...

IEEE2019

, ,

Part I of this paper developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to the larger set of locally balanced left-sto ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Exact Diffusion for Distributed Optimization and Learning-Part I: Algorithm Development

Ali H. Sayed, Bicheng Ying, Kun Yuan

This paper develops a distributed optimization strategy with guaranteed exact convergence for a broad class of left-stochastic combination policies. The resulting exact diffusion strategy is shown in Part II of this paper to have a wider stability range an ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Distributed Optimization and Control using Operator Splitting Methods

Georgios Stathopoulos

The significant progress that has been made in recent years both in hardware implementations and in numerical computing has rendered real-time optimization-based control a viable option when it comes to advanced industrial applications. At the same time, t ...

EPFL2018

Deep Learning for Logic Optimization Algorithms

Giovanni De Micheli, Sabine Süsstrunk, Frédéric Kaplan, Mathias Soeken, Winston Jason Haaswijk, Benoît Laurent Auguste Seguin, Edo Collins

The slowing down of Moore's law and the emergence of new technologies puts an increasing pressure on the field of EDA. There is a constant need to improve optimization algorithms. However, finding and implementing such algorithms is a difficult task, espec ...

IEEE2018