- Referenced in 305 articles
- algorithm (a “squared” conjugate gradient method) with a preconditioning called ILLU (an incomplete line...
- Referenced in 377 articles
- analytically equivalent to the standard method of conjugate gradients, but possesses more favorable numerical properties ... method, subroutine LSQR. Numerical tests are described comparing LSQR with several other conjugate-gradient algorithms...
- Referenced in 130 articles
- locally optimal block preconditioned conjugate gradient method: Toward the optimal preconditioned eigensolver: Locally optimal block ... preconditioned conjugate gradient method. We describe new algorithms of the locally optimal block preconditioned conjugate ... gradient (LOBPCG) method for symmetric eigenvalue problems, based on a local optimization of a three ... advocate the standard preconditioned conjugate gradient method for finding an eigenvector as an element...
- Referenced in 136 articles
- linear conjugate-gradient method (developed via the Lanczos method) in the solution of large-scale ... Lanczos characterization of the linear conjugate-gradient method may be exploited to define a modified ... iterations earlier. A preconditioned truncated Newton method is described that defines a search direction which ... direction defined by a nonlinear conjugate-gradient-type method and a modified Newton direction. Numerical...
- Referenced in 453 articles
- Method for Stochastic Optimization. We introduce Adam, an algorithm for first-order gradient-based optimization ... adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient ... invariant to diagonal rescaling of the gradients, and is well suited for problems that ... terms of data and/or parameters. The method is also appropriate for non-stationary objectives...
- Referenced in 617 articles
- chapters conclude with a demonstration of the methods discussed in the respective chapter using ... cases the noise often introduces artificial minimizers. Gradient information, even if available, cannot expected ... group. Implicit filtering methods use finite difference approximations of the gradient, which are adjusted ... conclude with a numerical demonstration of the methods discussed in the respective chapter, and with...
- Referenced in 111 articles
- constrained optimization problems. TRON uses a gradient projection method to generate ... Cauchy step, a preconditioned conjugate gradient method with an incomplete Cholesky factorization to generate...
- Referenced in 125 articles
- Algorithm 851: CG_DESCENT. A conjugate gradient method with guaranteed descent Recently, a new nonlinear ... conjugate gradient scheme was developed which satisfies the descent condition gTkdk ... extensive numerical tests and comparisons with other methods for large-scale unconstrained optimization are given...
- Referenced in 126 articles
- BiCGstab(l) of the bi-conjugate gradient method for the solution of a system...
- Referenced in 182 articles
- domain. At each iteration, a spectral gradient-projection method approximately minimizes a least-squares problem...
- Referenced in 85 articles
- SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives ... this work we introduce a new optimisation method called SAGA in the spirit ... SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA ... experimental results showing the effectiveness of our method...
- Referenced in 74 articles
- implementing the SPG method is introduced. SPG is a nonmonotone projected gradient algorithm for solving ... problems. It combines the classical projected gradient method with the spectral gradient choice of steplength...
- Referenced in 98 articles
- contrast, previous analyses of stochastic gradient descent methods for SVMs require Ω(1/ϵ2) iterations...
- Referenced in 60 articles
- equations are solved by a finite difference method; the fluid surface is represented ... surface are accurately imposed; the conjugate gradient method is employed for solving the discrete Poisson...
- Referenced in 124 articles
- ADAGRAD: adaptive gradient algorithm; Adaptive subgradient methods for online learning and stochastic optimization. We present ... family of subgradient methods that dynamically incorporate knowledge of the geometry of the data observed ... earlier iterations to perform more informative gradient-based learning. Metaphorically, the adaptation allows ... which employ proximal functions to control the gradient steps of the algorithm. We describe...
- Referenced in 39 articles
- NESUN - Nesterov’s universal gradient method: Universal gradient methods for convex optimization problems. In this...
- Referenced in 40 articles
- combination of Tikhonov regularization and the gradient method for solving nonlinear ill-posed problems ... presented. The TIGRA (Tikhonov-gradient method) algorithm proposed uses steepest descent iterations in an inner...
- Referenced in 51 articles
- nonsmooth split version of the Heavy-ball method from Polyak. A rigorous analysis ... prove convergence for several other gradient methods. First, an abstract convergence theorem for a generic...
- Referenced in 31 articles
- NeNMF: An optimal gradient method for non-negative matrix factorization. Nonnegative matrix factorization ... multiplicative update rule (MUR), the projected gradient method (PG), the projected nonnegative least squares (PNLS ... active set method (AS). However, they suffer from one or some of the following three ... problems. It applies Nesterov’s optimal gradient method to alternatively optimize one factor with another...
- Referenced in 30 articles
- fast proximal gradient, conditional gradient, subgradient and alternating projection methods. In particular, we present ... worst-case guarantee for the conditional gradient method by more than a factor ... also show how the optimized gradient method proposed by Kim and Fessler ... fast as the standard accelerated proximal gradient method...