Convex analysis and minimization algorithms

By J. Hiriart-Urruty, Claude Lemaréchal. 1993

Subfields: Optimization & Training, Algorithms & Complexity

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Citations in the corpus

Privacy Aware Learning (2012, methodology): “Using this mechanism, if we can characterize a unique distribution Q ∗ attaining the inﬁmum (4) for P ∗ (and by extension, for any P ), then we may study the effects of privacy between the method M and X .”
Dual Averaging for Distributed Optimization: Convergence Analysis and Network Scaling (2010, positive): “For instance, it holds for any convex function on a compact domain X , or for any polyhedral function on an arbitrary domain [HUL96a].”
Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk Minimization (2008, neutral): “In statistical machine learning and signal processing, divergences between probability distributions are frequently exploited as metrics to be optimized, such as in independent component analysis [6] and decentralized detection [25].”
A Universal Catalyst for First-Order Optimization (2015, background): “[11] J.”
Distributed subgradient methods and quantization effects (2008, neutral): “1For subgradient methods see, for example, [19], [22], [20], [8], [1], [2].”
Accelerated gradient methods for nonconvex nonlinear and stochastic programming (2013, neutral): “, [14]).”
Handbook of Semidefinite Programming (2000, methodology): “For a detailed introduction to convex analysis we refer to Stoer and Witzgall [803], Hiriart-Urruty and Lemarechal [373], or to Rockafellar [724].”
Incremental subgradient methods for nondifferentiable optimization (1999, methodology): “where d;,k is a subgradient of fi at xk, (Yk is a positive stepsize, and PX denotes projection on X. There is an extensive theory for this method (see Dem'yanov and Vasil'ev [DeV85], Shor [Sho85], Minoux [Min86], Polyak [Po187], Hiriart-Urruty and Lemarbchal [ HiL93 ], Bertsekas [Ber99]).”
Excessive Gap Technique in Nonsmooth Convex Minimization (2005, background): “(7.11) Problems of this type arise, for example, at each iteration of the bundle method [1].”
Two numerical methods for optimizing matrix stability (2002, methodology): “The method is inspired by the great success of gradient bundle methods for convex optimization [ 17 ].”
Bounded Linear Regularity, Strong CHIP, and CHIP are Distinct Properties (2000, methodology): “We adopt mostly standard notation from convex analysis as can be found in the classical [24] or the more recent [16, 17].”
Robust sparse coding for face recognition (2011, background): “η can be searched from 1 to 0 by the standard line-search process [8].”