Interior-point methods for optimization
TLDR
The current state of the art of interior point methods (IPMs) for convex, conic, and general nonlinear optimization is described in this paper, where the authors discuss the theory, outline the algorithms, and comment on the applicability of this class of methods.Abstract:
This article describes the current state of the art of interior-point methods (IPMs) for convex, conic, and general nonlinear optimization. We discuss the theory, outline the algorithms, and comment on the applicability of this class of methods, which have revolutionized the field over the last twenty years.read more
Citations
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Journal ArticleDOI
Nanophotonic particle simulation and inverse design using artificial neural networks
John Peurifoy,Yichen Shen,Li Jing,Yi Yang,Fidel Cano-Renteria,Brendan G. DeLacy,John D. Joannopoulos,Max Tegmark,Marin Soljacic +8 more
TL;DR: In this paper, artificial neural networks are used to approximate light scattering by multilayer nanoparticles. But the network needs to be trained on only a small sampling of the data to approximate the simulation to high precision.
Applications of Second Order Cone Programming
TL;DR: A significant special case of the problems which could be solved were those whose constraints were given by semidefinite cones, and these have a wide range of applications, some of which are discussed in Section 5, and can still be solved efficiently using interior point methods.
Proceedings Article
Optimization for Machine Learning
TL;DR: This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields and will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.
Proceedings Article
Online Learning With Predictable Sequences
TL;DR: In this article, the authors present methods for online linear optimization that take advantage of benign (as opposed to worst-case) sequences, where the sequence encountered by the learner is described well by a known predictable process.
Book ChapterDOI
Interior Point Methods for Nonlinear Optimization
Imre Pólik,Tamás Terlaky +1 more
TL;DR: After more than a decade of turbulent research, the IPM community reached a good understanding of the basics of IPMs and several books were published that summarize and explore different aspects of IPM's.
References
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Book
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Book
Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Book
Linear Matrix Inequalities in System and Control Theory
TL;DR: In this paper, the authors present a brief history of LMIs in control theory and discuss some of the standard problems involved in LMIs, such as linear matrix inequalities, linear differential inequalities, and matrix problems with analytic solutions.