Multiplier and gradient methods

By M. Hestenes. 1969

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Citations in the corpus

MRFalign: Protein Homology Detection through Alignment of Markov Random Fields (2014, methodology): “omputationally intractable to find the optimal solution of P1. Below we present an ADMM (Alternating Direction Method of Multipliers) method that can efficiently solve this problem to suboptimal. See [42] for a tutorial of the ADMM method. To use ADMM, we rewrite P1 as follows by making a copy of to”
Regularizing Text Categorization with Clusters of Words (2016, methodology): “Their method uses the alternating directions method of multipliers (Hestenes, 1969; Powell, 1969).”
Implementing bound constraints and total-variation regularization in extended full waveform inversion with the alternating direction method of multiplier: application to large contrast media (2019, methodology): “severely ill-conditioned. 2.1.2 IR-WRI augmented Lagrangian method To bypass this difﬁculty, IR-WRI implements the original constrained problem, equation 4, with the augmented Lagrangian (AL) method (Hestenes, 1969; Nocedal & Wright, 2006; Boyd et al., 2010; Bertsekas, 2016). min u;m max v 0+ vT”
Convex Optimization in Normed Spaces (2015, methodology): “This idea was introduced in [63] and [89], and combined with proximal iterations in [92].”
Augmented Lagrangian Method, Dual Methods, and Split Bregman Iteration for ROF, Vectorial TV, and High Order Models (2010, methodology): “Augmented Lagrangian method [23, 31, 32] has many advantages over other methods such as penalty method [1], and has been successfully applied to nonlinear PDEs and mechanics [21].”
Hashing for Distributed Data (2015, methodology): “In contrast, although with orthonormal columns, the matrix C is not squared in (1), which enables us to merge the two stages of ITQ.”
An immersogeometric variational framework for fluid–structure interaction: application to bioprosthetic heart valves (2014, methodology): “We consider an iterative approximation of the multiplier, based on the work of Hestenes [128] and Powell [129].”
A complementary energy formulation of no tension masonry-like solids (2000, methodology): “One of the most widely used versions of the augmented Lagrangian iteration (118) (120) is the Hestenes [24] and Powell [25] form.”
Data Assimilation for Numerical Weather Prediction: A Review (2009, methodology): “In the augmented Lagrangian algorithm (where the constrained problem is converted into a sequence of unconstrained minimization problems) we have L(ρ ,U,λ ) = J(U)+{λ ,F(U)}+ρ |F(U)|2 (56) This algorithm was initially proposed by Hestenes (1969) and independently by Powell (1969).”
Sparse and low-rank matrix decomposition via alternating direction method (2013, methodology): “In this section, we present experimental results to show the efficiency of ADM when applied to (1.1).”
Convex Optimization in Normed Spaces: Theory, Methods and Examples (2015, methodology): “This idea was introduced in [63] and [89], and combined with proximal iterations in [92].”
Linear Convergence Rate of a Class of Distributed Augmented Lagrangian Algorithms (2013, methodology): “The method of multipliers based on the augmented Lagrangian has been proposed in the late 1960s [34], [35].”
Linearized augmented Lagrangian and alternating direction methods for nuclear norm minimization (2012, methodology): “The classical augmented Lagrangian method (also known as the method of multipliers, see, e.g., [25, 39, 46]) is also discussed in [40] for low-rank matrix recovery problems based on this UV -parametrization.”
Monotone Operators and the Proximal Point Algorithm (1976, methodology): “• The second type of application corresponds to the "method of multipliers" of Hestenes [8] and Powell [21].”