Projected Barzilai-Borwein methods for large-scale box-constrained quadratic programming

By Yuhong Dai, Roger Fletcher. Numerische Mathematik, 2005

379 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Control and Systems Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/121f7e18160992b1952433d36f2c74fb036f6011

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Citations in the corpus

Barzilai-Borwein Step Size for Stochastic Gradient Descent (2016, methodology): “For convergence analysis, generalizations and variants of the BB method, we refer the interested readers to [14, 15, 6, 9, 4, 5, 3] and references therein.”
Single disperser design for coded aperture snapshot spectral imaging. (2008, methodology): “This approach is based on a variant of the Barzilai–Borwein gradient projection method [21] and has code available online [22] .”
A feasible method for optimization with orthogonality constraints (2012, background): “Since the BB step size does not necessarily decrease the objective value at every iteration, it may invalidate convergence, but this issue can be solved by introducing a globalization technique, which guarantees global convergence by regulating the step sizes in (28) only occasionally; see [14,44].”
Probing the Pareto Frontier for Basis Pursuit Solutions (2008, methodology): “Their approach builds on the earlier report by Dai and Fletcher [17] on the efficiency of a specialized SPG method for general bound-constrained quadratic programs (QPs).”
Sparse Reconstruction by Separable Approximation (2008, methodology): “BB methods have also been applied to constrained problems [2], especially bound-constrained quadratic programs [7, 15, 22].”
On spectral properties of steepest descent methods (2013, methodology): “A deeper analysis of the asymptotic behaviour of BB and related methods is proposed in Dai & Fletcher (2005).”
New adaptive stepsize selections in gradient methods (2008, methodology): “Furthermore, successful extensions of these BB-like gradient methods to non-quadratic functions [10, 15] and to constrained optimization problems [3, 7, 8, 9, 18, 21] have been proposed.”
The cyclic Barzilai-–Borwein method for unconstrained optimization (2006, methodology): “The analysis in Dai & Fletcher (2005a) shows that if m > n2 , cyclic SD is likely R-superlinearly convergent.”
Sample size selection in optimization methods for machine learning (2012, methodology): “For the subspace phase, one could minimize FS [17, 9] instead of a quadratic model of this function [8, 20], but we choose to work with a model due to the high cost of evaluating the objective function.”
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems (2007, methodology): “We also tried other variants of the Barzilai-Borwein approach, includin g one proposed in [15], which alternates between two definitions o f α.”
11 Projected Newton-type Methods in Machine Learning (2011, background): “Indeed, due to its strong empirical performance, SPG has recently also been explored in several other applications (Dai and Fletcher, 2005; Figueiredo et al., 2007; van den Berg and Friedlander, 2008).”
Optimizing Costly Functions with Simple Constraints: A Limited-Memory Projected Quasi-Newton Algorithm (2009, neutral): “Due to its strong empirical Algorithm 2 : Spectral Projected Gradient Algorithm performance and simplicity there has recently been a growing interest in the SPG method and it has been used successfully in several applications (e.g., van den Berg and Friedlander (2008); Dai and Fletcher (2005)).”