Parallel Optimization: Theory, Algorithms and Applications

By A. Stachurski. Parallel Distributed Comput. Pract., 2000

673 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Industrial and Manufacturing Engineering

View Paper: https://www.semanticscholar.org/paper/da45065be36213069eec538159138b7bc49cd208

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Citations in the corpus

Survey on distance metric learning and dimensionality reduction in data mining (2014, methodology): “For parallel/distributed distance metric algorithms, as the major computational techniques involved are eigenvalue decomposition and quadratic programming, we can adopt parallel matrix computation/optimization algorithms (Modi et al. 1989; Censor 1997) to make distance metric learning more scalable ”
Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces (2003, background): “(31) and (35), we get jlðzT yn1Þj 8 1 , jlðyn2Þj 8 1 , and jlðzT SnxÞj 2 1 because klk ¼ 1: œ 502 Butnariu, Reich, and Zaslavski Now we are in a position to prove a result which shows that in the spaceMfu ðKÞ weak convergence of the orbits is a generic property.”
High-dimensional covariance estimation by minimizing ℓ1-penalized log-determinant divergence (2008, background): “A function is of Bregman type if it is strictly convex, continuously differentiable and has bounded level sets [4, 7].”
A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization (2012, positive): “Due to its particular simple implementation, the BCD method as been widely used for solving problems such as power allocation in wireless communication systems [28], clustering [14], image denoising and image reconstruction [7] and dynamic programming [17].”
Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers (2011, neutral): “Some good reference books on parallel optimization include those by Bertsekas and Tsitsiklis [17] and Censor and Zenios [31].”
Learning from Multiple Sources (2006, methodology): “We refer the reader to [8] for more details about Bregman divergences and to [9] for more information about exponenti al families.”
A Hierarchical Presentation of Operators with Fixed Points on Hilbert Spaces (2006, background): “We mention the names of paracontraction, general paracontraction, strict paracontraction [6, 7, 10, 11, 14], Q -quasi-nonexpansive, strongly Q -quasinonexpansive, and Q -pseudo-contractive [19].”
Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization (2001, background): “Since we have also that (7) holds with jGl, we see that (9) holds for jGl.”
The Interplay Between Stability and Regret in Online Learning (2012, background): “2 Bregman Divergences and Strong Convexity Here we recall the definition of a Bregman divergence [5, 6] which finds use in online learning algorithms.”
On the Algorithmic Implementation of Multiclass Kernel-based Vector Machines (2002, background): “However, the roots of this line of research go back to the seminal work of Lev Bregman (1967) which was further developed by Yair Censor and colleagues (see Censor and Zenios, 1997 for an excellent overview).”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “This model covers numerous signal and image restoration and reconstruction prescriptions [2, 16, 23, 39, 66, 67].”
Logistic Regression, AdaBoost and Bregman Distances (2000, neutral): “SeealsoCsisźar’s survey article[10] aswell asCensorandZenios’ s book[5].”
Online Large-Margin Training of Dependency Parsers (2005, methodology): “This can be formalized by substituting the following update into line 4 of the generic online algorithm, This is a standard quadratic programming problem that can be easily solved using Hildreth’s al-gorithm (Censor and Zenios, 1997).”
Efficient sparse coding algorithms (2006, methodology): “In general, this constrained optimization problem can be solved using gradient descent with iterative projection [10].”
Log-Euclidean Metric Learning on Symmetric Positive Definite Manifold with Application to Image Set Classification (2015, methodology): “To solve the optimization problem in Eq.8, we adopt the cyclic Bregman projection algorithm (Bregman, 1967; Censor & Zenios, 1997), which is to choose one constraint per iteration, and perform a projection so that the current solution satisfies the chosen constraint.”
Bregman Alternating Direction Method of Multipliers (2013, methodology): “Proximal point method with D-functions (PMD) [6, 5] and Breg-man proximal minimization (BPM) [20] generalize proximal point method by using generalized Bregman divegence to replace the quadratic term.”
Proximal Splitting Methods in Signal Processing (2009, neutral): “This reduces (1) to the classical convex feasibility problem[28], [38], [40], [83], [90], [114], [115], [120], [133] find x ∈ m ⋂”