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165,342
Just Relax: Convex Programming Methods for Identifying Sparse Signals in Noise
, 2006
"... This paper studies a difficult and fundamental problem that arises throughout electrical engineering, applied mathematics, and statistics. Suppose that one forms a short linear combination of elementary signals drawn from a large, fixed collection. Given an observation of the linear combination that ..."
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Cited by 496 (2 self)
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. This paper studies a method called convex relaxation, which attempts to recover the ideal sparse signal by solving a convex program. This approach is powerful because the optimization can be completed in polynomial time with standard scientific software. The paper provides general conditions which ensure
Graph implementations for nonsmooth convex programs
 Recent Advances in Learning and Control, Lecture Notes in Control and Information Sciences
, 2008
"... Summary. 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 a very wide variety of smooth and nonsmooth convex programs to be easily specified and effi ..."
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Cited by 248 (7 self)
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Summary. 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 a very wide variety of smooth and nonsmooth convex programs to be easily specified
Online Convex Programming and Generalized Infinitesimal Gradient Ascent
, 2003
"... Convex programming involves a convex set F R and a convex function c : F ! R. The goal of convex programming is to nd a point in F which minimizes c. In this paper, we introduce online convex programming. In online convex programming, the convex set is known in advance, but in each step of some ..."
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Cited by 288 (4 self)
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Convex programming involves a convex set F R and a convex function c : F ! R. The goal of convex programming is to nd a point in F which minimizes c. In this paper, we introduce online convex programming. In online convex programming, the convex set is known in advance, but in each step
Fisher Markets and Convex Programs
"... Convex programming duality is usually stated in its most general form, with convex objective functions and convex constraints. (The book by Boyd and Vandenberghe is an excellent reference [2].) At this ..."
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Cited by 2 (1 self)
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Convex programming duality is usually stated in its most general form, with convex objective functions and convex constraints. (The book by Boyd and Vandenberghe is an excellent reference [2].) At this
A globally convergent primaldual interior point algorithm for convex programming
 Mathematical Programming 64
, 1994
"... for convex programming ..."
Exact regularization of convex programs
, 2007
"... The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only if a ..."
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Cited by 27 (1 self)
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The regularization of a convex program is exact if all solutions of the regularized problem are also solutions of the original problem for all values of the regularization parameter below some positive threshold. For a general convex program, we show that the regularization is exact if and only
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5350 (67 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Posture recognition with convex programming
"... We present a novel human posture recognition method us ing convex programming based matching schemes. Instead of trying to segment the object from the background, we develop a novel multistage linear programming scheme to locate the target by searching for the best matching region based on an automa ..."
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Cited by 2 (2 self)
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We present a novel human posture recognition method us ing convex programming based matching schemes. Instead of trying to segment the object from the background, we develop a novel multistage linear programming scheme to locate the target by searching for the best matching region based
Convex Programming for Disjunctive Convex Optimization
, 1998
"... Given a finite number of closed convex sets whose algebraic representation is known, we study the problem of optimizing a convex function over the closure of the convex hull of the union of these sets. We derive an algebraic characterization of the feasible region in a higherdimensional space and p ..."
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Cited by 30 (0 self)
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and propose a solution procedure akin to the interiorpoint approach for convex programming. Research partly supported by NSF HPCC Grant DMS 9527124. Author's address: 417 Uris Hall, Graduate School of Business, Columbia University, New York NY 10027. Email sebas@cumparsita.gsb.columbia.edu. Also
On Conically Ordered Convex Programs
, 2003
"... In this paper we study a special class of convex optimization problems called conically ordered convex programs (COCP), where the feasible region is given as the level set of a vectorvalued nonlinear mapping, expressed as a nonnegative combination of convex functions. The nonnegativity of the vect ..."
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Cited by 3 (2 self)
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In this paper we study a special class of convex optimization problems called conically ordered convex programs (COCP), where the feasible region is given as the level set of a vectorvalued nonlinear mapping, expressed as a nonnegative combination of convex functions. The nonnegativity
Results 1  10
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