Interior Gradient and Proximal Methods for Convex and Conic Optimization

By Alfred Auslender, Marc Teboulle. SIAM Journal on Optimization, 2006

315 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/02735841eca4cf224b874673086429956d092e0d

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Citations in the corpus

Subgradient Methods for Saddle-Point Problems (2009, methodology): “We start by introducing the notation and basic terminology that we use throughout the paper.”
Optimal Stochastic Approximation Algorithms for Strongly Convex Stochastic Composite Optimization, II: Shrinking Procedures and Optimal Algorithms (2013, background): “2) to other distance-like functions can be found, for example, in [1, 2].”
Algorithms for stochastic optimization with expectation constraints (2016, background): “[1] Alfred Auslender and Marc Teboulle.”
Primal-dual first-order methods with $${\mathcal {O}(1/\epsilon)}$$ iteration-complexity for cone programming (2011, methodology): “A proximal-point-type algorithm for (1) having the same complexity above has also been proposed more recently by Auslender and Teboulle [1].”
An optimal method for stochastic composite optimization (2011, methodology): “In particular, Auslender and Teboule [1] give a more geometrically transparent definition for this notion.”
Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, background): “Other related approaches include [17], [65] and [51].”
Convex Optimization in Normed Spaces (2015, background): “Other related approaches include [17], [65] and [51].”
Smoothing and First Order Methods: A Unified Framework (2012, methodology): “For instance, the methods in [17, 18] requires two proximal steps based on two different proximal terms per iteration and accumulated memory of previous gradients, while the methods described in [4, 8] request only one proximal-based computation per iteration, thus providing computational saving.”
Approximation accuracy, gradient methods, and error bound for structured convex optimization (2010, methodology): “This method, which we call the proximal gradient (PG) method, is closely related to the mirror descent method of Nemirovski and Yudin [93], as is discussed in [8,12]; also see [61] for the case of η(·) = 1 2‖ · ‖(2)2.”
Fast L1-Minimization Algorithms For Robust Face Recognition (2010, unknown): “Therefore, the following iterative scheme can be constructed to update the primal and dual variables based on the ﬁrst-order projected gradient methods proposed in [62], [63]: where { t k } is a sequence of step sizes satisfying t k ≤ µ/ (cid:107) A T A (cid:107) for all k .”
Sketchy Decisions: Convex Low-Rank Matrix Optimization with Optimal Storage (2017, methodology): “er memory scaling than other convex optimization methods. We compare ve convex optimization algorithms: the classic proximal gradient method (PGM) [32]; the Auslender{Teboulle (AT) accelerated method [2]; the classic CGM algorithm [23]; a storage-ecient CGM variant (ThinCGM) [39] based on low-rank S”
Proximal Newton-Type Methods for Minimizing Composite Functions (2012, methodology): “timal ﬁrst-order methods, also called accelerated ﬁrst-order methods[20], which achieve an O( 1 k2) convergence rate. The two most popular methods 1 in this family are Auslender and Teboulle’s method [1] and Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), by Beck and Teboulle [2]. These met”
A Descent Lemma Beyond Lipschitz Gradient Continuity: First-Order Methods Revisited and Applications (2017, methodology): “Our analysis builds on Güler [24] initially developed for the classical quadratic proximal minimization method, and follows its extensions in Chen and Teboulle [15] and Auslender and Teboulle [1].”
Primal-dual first-order methods with O (1/e) iteration-complexity for cone programming. (2011, methodology): “A proximal-point-type algorithm for (1) having the same complexity above has also been proposed more recently by Auslender and Teboulle [1].”
Adaptation, Learning, and Optimization over Networks (2014, methodology): “The temporal step is reminiscent of momentum-type techniques proposed for gradient descent optimization [11, 21, 177, 178]”
Adaptive Restart for Accelerated Gradient Schemes (2012, methodology): “In recent years there has been a resurgence of interest in first-order optimization methods [1, 3, 14, 20, 24], driven primarily by the need to solve very large problem instances unsuited to second-order methods.”
Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization (2013, background): “It is well-known that using a generalized distance generating function, instead of the usual Euclidean distance function, would lead to algorithms that can be adjusted to the geometry of the feasible set and/or efficient solutions of the projection [2,3,5,21,26, 38].”
Templates for convex cone problems with applications to sparse signal recovery (2010, methodology): “After some experimentation, we concluded that the Auslender and Teboulle first-order variant [2,63] is a good choice for this model.”
Convex optimization under inexact first-order information (2009, methodology): “2, which was studied by Bregman [10] and many others (see [1, 2, 29, 72] and references therein).”
The Complexity of Large-scale Convex Programming under a Linear Optimization Oracle (2013, background): “More speciﬁcally, for a given strongly convex function (3.15) Note that V ( y ) is often referred to as the Bregman distance (from y to c v ) in the literature, which was initially studied by [8] and later by many others (see [2,4,33,37] and references therein).”