Convex Optimization in Signal Processing and Communications

By D. P. Palomar, Yonina C. Eldar. 2009

614 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Networks and Communications, Signal Processing

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In Computational Mechanics

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Citations in the corpus

Hyperparameter optimization with approximate gradient (2016, background): “As convergence criterion, we consider the norm of the (scaled) gradient mapping , a generalization of the gradient that ensures convergence to a stationary point (Beck and Teboulle, 2009, §1.4.4).”
Generalized Sparse Additive Models (2019, methodology): “In many cases, this algorithm has a per-iteration complexity of O ( np ) — precisely that of state-of-the-art algorithms for the lasso [Friedman et al., 2010, Beck and Teboulle, 2009b].”
Distributed Alternating Direction Method of Multipliers (2012, methodology): “These problems motivated research interest in developing distributed method for solving optimization problems [4], [7], [12], [13], [15], [18], [19].”
Templates for convex cone problems with applications to sparse signal recovery (2010, methodology): “The forward-backward algorithm has been extensively studied, and in our finite dimensional setting, it is known that the variable zk converges [4,24]; in contrast, there is no general result proving the convergence of zk for the optimal algorithms.”
Asymptotic behavior of unregularized and ridge-regularized high-dimensional robust regression estimators : rigorous results (2013, positive): “The proximal mapping is an important notion in convex analysis and convex optimization (see for instance Beck and Teboulle (2010) for a nice review of analytic properties and an introduction to proximal gradient algorithms).”
"Convex Until Proven Guilty": Dimension-Free Acceleration of Gradient Descent on Non-Convex Functions (2017, methodology): “Adaptive restart accelerated gradient descent We use the accelerated gradient descent scheme of Beck and Teboulle (2009) with ωt = t/(t + 3).”
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications (2017, background): “, [29, 34] and references therein for an appetizer.”
Prox-PDA: The Proximal Primal-Dual Algorithm for Fast Distributed Nonconvex Optimization and Learning Over Networks (2017, methodology): “We compare the the Prox-GPDA, and Prox-GPDA-IP with the distributed subgradient (DSG) method (Nedic & Ozdaglar, 2009a;b) (which is only known to work for convex cases) and the Push-sum algorithm (Tatarenko & Touri, 2015).”
SINR-Based DoS Attack on Remote State Estimation: A Game-Theoretic Approach (2017, background): “Therefore, these two objective functions will lead to different solutions due to the well-known inequality [23] max x min y f ( x, y ) (cid”
Proximal Splitting Algorithms: A Tour of Recent Advances, with New Twists. (2020, background): “Many problems in statistics, machine learning, signal and image processing, or control can be formulated as convex optimization problems [1–7].”
Model-Based Deep Learning (2020, background): “6(d) which demonstrates that the trained unfolded network can achieve with only a few layers an MSE accuracy which the model-based fast ISTA of [54], [55] does not approach even in 50 iterations.”
Joint Transmit Beamforming for Multiuser MIMO Communications and MIMO Radar (2019, methodology): “In this subsection, we tackle the non-convex problem (26) using an SDR strategy [60], [61].”
Asynchronous Broadcast-Based Convex Optimization Over a Network (2011, background): “The agent (that has just updated the iterate) passes the iterate to a randomly selected neighbor to perform the next update.”
Robust Recovery of Signals From a Structured Union of Subspaces (2008, background): “The most common type of sampling is linear sampling in which yi = 〈si, x〉, 1 ≤ i ≤ n, (1) for a set of functionssi ∈ H [4], [31]–[37].”
Breaking the Nonsmooth Barrier: A Scalable Parallel Method for Composite Optimization (2017, methodology): “This is a direct consequence of the first order optimality conditions on the definition of proximal operator, see e.g. (Beck & Teboulle, 2009; Nesterov, 2013).”