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Convex Optimization
A comprehensive introduction to the subject of convex optimization shows in detail how such problems can be solved numerically with great efficiency. Expand
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
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. Expand
Enhancing Sparsity by Reweighted ℓ1 Minimization
A novel method for sparse signal recovery that in many situations outperforms ℓ1 minimization in the sense that substantially fewer measurements are needed for exact recovery. Expand
Randomized gossip algorithms
This work analyzes the averaging problem under the gossip constraint for an arbitrary network graph, and finds that the averaging time of a gossip algorithm depends on the second largest eigenvalue of a doubly stochastic matrix characterizing the algorithm. Expand
Proximal Algorithms
The many different interpretations of proximal operators and algorithms are discussed, their connections to many other topics in optimization and applied mathematics are described, some popular algorithms are surveyed, and a large number of examples of proxiesimal operators that commonly arise in practice are provided. Expand
Semidefinite Programming
A survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution are given. Expand
Graph Implementations for Nonsmooth Convex Programs
We describe graph implementations, a generic method for representing a convex function via its epigraph, described in a disciplined convex programming framework. This simple and natural idea allows aExpand
A tutorial on geometric programming
Abstract A geometric program (GP) is a type of mathematical optimization problem characterized by objective and constraint functions that have a special form. Recently developed solution methods canExpand
Applications of second-order cone programming
In a second-Order cone program (SOCP) a linear function is minimized over the intersection of an affine set and the product of second-Order (quadratic) cones. SOCPs are nonlinear convex Problems thatExpand