Open AccessBook
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TLDR
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.Abstract:
Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can be solved numerically with great efficiency. The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. The text contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance, and economics.read more
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Book
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
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Cognitive radio: brain-empowered wireless communications
TL;DR: Following the discussion of interference temperature as a new metric for the quantification and management of interference, the paper addresses three fundamental cognitive tasks: radio-scene analysis, channel-state estimation and predictive modeling, and the emergent behavior of cognitive radio.
Book
Gaussian Processes for Machine Learning
TL;DR: The treatment is comprehensive and self-contained, targeted at researchers and students in machine learning and applied statistics, and deals with the supervised learning problem for both regression and classification.
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Robust Face Recognition via Sparse Representation
TL;DR: This work considers the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise, and proposes a general classification algorithm for (image-based) object recognition based on a sparse representation computed by C1-minimization.
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Signal Recovery From Random Measurements Via Orthogonal Matching Pursuit
Joel A. Tropp,Anna C. Gilbert +1 more
TL;DR: It is demonstrated theoretically and empirically that a greedy algorithm called orthogonal matching pursuit (OMP) can reliably recover a signal with m nonzero entries in dimension d given O(m ln d) random linear measurements of that signal.
References
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A new polynomial-time algorithm for linear programming
TL;DR: It is proved that given a polytopeP and a strictly interior point a εP, there is a projective transformation of the space that mapsP, a toP′, a′ having the following property: the ratio of the radius of the smallest sphere with center a′, containingP′ to theradius of the largest sphere withCenter a′ contained inP′ isO(n).
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The interior-point revolution in optimization: History, recent developments, and lasting consequences
TL;DR: A condensed, unavoidably incomplete look at classical material and recent research about interior methods shows how interior methods have continued to transform both the theory and practice of constrained optimization.
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Linear systems in Jordan algebras and primal-dual interior-point algorithms
TL;DR: In this article, a non-degeneracy theory for interior point interior-point problems is proposed. But the non-egeneracy problem is not considered in this paper, and the question of solvability of a linear system arising in the implementation of the primal-dual algorithm is analyzed.
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Euclidean Jordan Algebras and Interior-point Algorithms
TL;DR: In this article, a short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered.
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Primal-dual algorithms and infinite-dimensional Jordan algebras of finite rank
TL;DR: It is shown that this algorithm can be generalized along with complexity estimates to the infinite-dimensional situation under consideration, and an application is given to an important problem of control theory: multi-criteria analytic design of the linear regulator.