Minimization Methods for Non-Differentiable Functions

By N. Shor. 1985

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Citations in the corpus

Network Topology and Communication-Computation Tradeoffs in Decentralized Optimization (2017, background): “10Under weaker assumptions on the stepsize than those of Theorem 7, namely α k → 0 and ∑ k=0 ∞ α k = ∞ , one can show that lim inf k→∞ h( x k ) = h * , where h * = inf x∈ R d h(x) ; see [1], [43], and [44].”
Learning from Demonstrations: Is It Worth Estimating a Reward Function? (2013, methodology): “The minimization is realized via a sub-gradient descent [9].”
First-order methods of smooth convex optimization with inexact oracle (2013, unknown): “[21, 20, 2, 10] for subgradient methods, and [2, 7, 8] for proximal point and bundle methods).”
Prediction with Model-Based Neutrality (2013, methodology): “In our experiments with η-neutral logistic regression, we used Shor’s ralgorithm based on adaptive space dilation [13].”
Time and Space: Why Imperfect Information Games are Hard (2018, methodology): “We must also use a different scheme for selecting the step size, either by selecting η as function of the desired error, or by using a decreasing sequence ηt resulting in a convergence rate of O(1/ε(2)) [80, 35].”
Structured Learning and Prediction in Computer Vision (2011, methodology): “However, subgradient methods [139] that we introduced in Section 4.”
Dual methods for nonconvex spectrum optimization of multicarrier systems (2006, background): “A common criterion for choosing the step sizes is that must be square summable, but not absolute summable [25], [26].”
1 Introduction to Dual Decomposition for Inference (2010, methodology): “22) when solving a Lagrangian relaxation using subgradient methods has been well-studied (e.g., see Anstreicher and Wolsey, 2009; Nedić and Ozdaglar, 2008; Shor et al., 1985).”
Parallel Multi-Block ADMM with o(1 / k) Convergence (2013, unknown): “1) is dual decomposition [9], which is essentially a dual ascent method or dual subgradient method [28] as follows.”
Online) Subgradient Methods for Structured Prediction (2007, methodology): “This objective is then optimized by a direct generalization of gradient descent, popular in convex optimization, called the subgradient method (Shor, 1985).”