Review of 'Numerical Optimization' by Bonnans, Gilbert, LemarÃ©chal and Sagastizabal

By D. Griffel. 2004

1,639 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Computational Mechanics, Computational Theory and Mathematics, Evaluation & Benchmarks

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The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Computational Mechanics

In Computational Theory and Mathematics

In Evaluation & Benchmarks

Citations in the corpus

Trust Region Policy Optimization (2015, positive): “One could alternatively use a generic method for calculating Hessian-vector products using reverse mode automatic differentiation ((Wright & Nocedal, 1999), chapter 8), computing the Hessian of D KL with respect to θ .”
Gradient Estimation Using Stochastic Computation Graphs (2015, neutral): “The Hessian-vector product can be used to implement a quasi-Newton algorithm via the conjugate gradient algorithm [28].”
From Pixels to Torques: Policy Learning with Deep Dynamical Models (2015, positive): “The cost functions are then minimized by the BFGS algorithm (Nocedal & Wright, 2006).”
Rethinking LDA: Moment Matching for Discrete ICA (2015, neutral): “We explain how we initialize the parameter c 0 for the LDA moments in Appendix G.3.”
Identifying and attacking the saddle point problem in high-dimensional non-convex optimization (2014, neutral): “This can be done regardless of the approximation strategy used for the Newton method such as a truncated Newton method or a BFGS approximation (see Nocedal and Wright (2006) chapters 4 and 7).”
Optimizing Neural Networks with Kronecker-factored Approximate Curvature (2015, positive): “…natural gradient-based optimization methods can conversely be viewed as 2nd-order optimization methods, which as pointed out by Martens (2014)), brings to bare the vast wisdom that has accumulated about how to make such methods work well in both theory and practice (e.g Nocedal and Wright, 2006).”
Entropy Search for Information-Efficient Global Optimization (2011, neutral): “Thor-ough introductions can be found in the textbooks by Nocedal and Wright (1999) and Boyd and Vandenberghe (2004).”
Escaping From Saddle Points - Online Stochastic Gradient for Tensor Decomposition (2015, neutral): “Please refer to Wright and Nocedal (1999) for the proof of those theorems.”
Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning (2014, neutral): “g, [5, 8, 10, 46].”
Shallow Parsing with Conditional Random Fields (2003, positive): “A more detailed description of this method can be found elsewhere (Nocedal and Wright, 1999).”
Tensor decompositions for learning latent variable models (2012, neutral): “(The more general case allows the weights wi in M2 to differ in M3, but for simplicity we keep them the same in the following discussion.)”
Lower bound limit analysis of cohesive‐frictional materials using second‐order cone programming (2006, neutral): “Reference [54]) is satisfied at the apex point xx = yy = c cot , xy = 0.”
Bundle Adjustment in the Large (2010, positive): “Typically an iterative linear solver like the Conjugate Gradients method is used for this purpose [11].”
Generalized additive and index models with shape constraints (2014, positive): “Our aim is to reformulate the problem as a convex program in terms of basis functions and to apply an active set algorithm (Nocedal and Wright, 2006).”
Continuous Time Dynamic Topic Models (2008, positive): “Finally, we note that we use the conjugate gradient algorithm [16] to optimize the variational observations from these partial derivatives.”
Acoustic emission source localization and velocity determination of the fundamental mode A0 using wavelet analysis and a Newton-based optimization technique (2010, neutral): “…the objective function   x F with respect to the four unknowns of the problem: Newton’s method can be modified and enhanced in various ways for solving systems of non linear equations, but in particular conditions, when the starting point is not near the root, it may not converge (Nocedal, 1999).”
Sourcebook of parallel computing (2003, neutral): “, [257, 715]), including line-search and trust-region variants.”