Convex Analysis And Nonlinear Optimization

By Jonathan Michael Borwein, A. S. Lewis. 2000

1,472 citations recorded by the source corpus.

Subfields: Numerical Analysis, Mathematical Optimization

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Citations in the corpus

Bridging the Gap Between Value and Policy Based Reinforcement Learning (2017, background): “Since F τ is closed and convex, we also have that F τ = F ∗∗ τ (Borwein & Lewis, 2000, Section 4.2); hence Lemma 9.”
DeepMDP: Learning Continuous Latent Space Models for Representation Learning (2019, background): “Pinsker’s inequality (Borwein & Lewis, 2005, p.63) bounds the TV with the Kullback–Leibler (KL) divergence.”
Optimization with Sparsity-Inducing Penalties (2011, background): “4) is known to belong to the normal cone to B = {w ∈ Rp; Ω(w) ≤ μ} at ŵ [20].”
Regularization Techniques for Learning with Matrices (2009, methodology): “Cavallanti et al. [2008], Agarwal et al. [2008]), and online PCA [Warmuth and Kuzmin, 2006]. It was also studied under the framework of group Lasso (e.g. Yuan and Lin [2006], Obozinski et al. [2007], Bach [2008]). In the context of learning vectors (rather than matrices), the study of the relative p”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “This implies that the Fenchel-conjugates ψ∗ j (which are already differentiable because of the strict convexity of ψj [28]) are defined and finite on R; moreover, since each ψk is continuously differentiable, each ψ∗ k is strictly convex.”
Distributed Kalman filtering based on consensus strategies (2008, background): “Hence, it follows from the theory of convex spectral functions that also J is a convex function [5].”
Fixed point and Bregman iterative methods for matrix rank minimization (2009, neutral): “, [1; 4]) ∂‖X‖∗ = {UV⊤+W : U⊤W = 0,WV = 0,‖W‖ ≤ 1}.”
An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares (2007, background): “…well as new equality constraints , to obtain the equivalent problem (9) Associating dual variables with the equality constraints , the Lagrangian is The dual function is The Lagrange dual of (9) is therefore (10) where the dual objective is (See, e.g., [3, ch. 5] or [2] for more on convex duality.)”
Generalized Low Rank Models (2014, background): “t = 1/t, which guarantees convergence to the globally optimal X if Y is fixed [12, 18].”
Optimality conditions for non-smooth semi-infinite programming (2010, background): “The bipolar theorem [2] states that A 1⁄4 coneðAÞ: We first recall the notions of the contingent cone and the cone feasible directions.”