Constrained minimization methods

By E. Levitin, Boris Polyak. 1966

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In Optimization & Training

Citations in the corpus

Affine Invariant Analysis of Frank-Wolfe on Strongly Convex Sets (2020, methodology): “1 shows an affine invariant linear rate of convergence of FW, generalizing existing convergence results of Frank-Wolfe on strongly convex sets [Levitin et al. 1966; Demyanov et al. 1970; Dunn 1979].”
Frank-Wolfe Algorithms for Saddle Point Problems (2016, background): “Frank-Wolfe for convex optimization over strongly convex sets has been studied by Levitin and Polyak (1966); Demyanov and Rubinov (1970) and Dunn (1979), amongst others.”
On the Global Linear Convergence of Frank-Wolfe Optimization Variants (2015, methodology): “The early work of [23] showed linear convergence for strongly”
Walking in the Shadow: A New Perspective on Descent Directions for Constrained Minimization (2020, methodology): “The vanilla Conditional Gradient method (CG) or the Frank-Wolfe algorithm (FW) [9, 12] has received a lot of interest from the ML community mainly because of its iteration complexity, tractability and sparsity of iterates.”
Projection-Free Adaptive Gradients for Large-Scale Optimization (2020, methodology): “The Frank-Wolfe algorithm (FW) (Frank and Wolfe, 1956), a.k.a. conditional gradient algorithm (Levitin and Polyak, 1966), is a simple projection-free first-order algorithm for constrained minimization.”
Newton-Kantorovich Method and Its Global Convergence (2006, unknown): “This result was obtained in [43]; for more details and examples, see [44, 45].”
Interior-Point Gradient Method for Large-Scale Totally Nonnegative Least Squares Problems (2005, background): “Again, by substitution we calculate α = (e − u) Diag(x ◦ A Ax)(e − u) (e − u)T Diag(x)(AT A)Diag(x)(e − u) , (4) where Diag(x) is the diagonal matrix with the vector x on its diagonal (similarly for the other diagonal matrix), e is the vector of all ones, and ui = (A T b)i/(A T Ax)i.”
Linear-Memory and Decomposition-Invariant Linearly Convergent Conditional Gradient Algorithm for Structured Polytopes (2016, methodology): “rder methods, e.g., the projected gradient method. It is known, already from the rst introduction of the method by Frank and Wolfe in the 1950’s [5], and the somewhat later work of Polyak and Levitin [20], that the method converges with a rate of roughly O(1=t) for minimizing a smooth convex functio”
Outer approximation methods for solving variational inequalities in Hilbert space (2017, methodology): “This method appeared in the literature as the gradient projection method in the context of minimization and was introduced by Goldstein [8], and Levitin and Polyak [9].”
Hybrid Steepest Descent Method for Variational Inequality Problem over the Fixed Point Set of Certain Quasi-nonexpansive Mappings (2005, background): “Several convergence analyses on (13) are found for example in Dolidze (1982), Goldstein (1964), Golshtein and Tretyakov (1996), Levitin and Polyak (1966), and Zeidler (1985, 1990).”
On the linear convergence of the alternating direction method of multipliers (2012, unknown): “Popular choices for the ascent methods include (single) coordinate ascent (see [3,7,9,31,38,40,46,47,53]), gradient ascent (see [31,40,48]) and gradient projection [22,29].”