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Some well-known formulas for (beta_{k}) include the Fletcher-Reeves (FR) [1], the Polak-Ribière-Polyak (PRP) [2, 3], the Liu-Storey (LS) [4], the Dai-Yuan (DY) [5], the Hestenes-Stiefel (HS) [6] and the conjugate descent (CD) [7] formulas.
Instead, Zhang et al. proposed an algorithm similar to conjugate descent to solve this problem [22], alternating between (a) training the linear separator given current label assignments and (b) updating the label assignment based on the linear separator.
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During the minimization, conjugate-descent and steepest-descent algorithms were employed.
Conjugate gradient descent algorithms have been used in several magnetohydrodynamic (MHD) equilibrium codes to find numerical minima of the MHD energy and thus to locate local stable equilibria.
Motivated by the special structure of partial Fourier transform in sparse MRI, this algorithm is accelerated by the preconditioned conjugate gradient descent method.
A unique set of sound sources is finally recovered by searching for that rotation (by conjugate gradient descent in the Stiefel manifold of unitary matrices) which maximizes their spatial compactness, as measured either by their spatial variance or their spatial entropy.
Neural network model was prepared and trained with training algorithm Conjugate Gradient Descent (CGD) to compute discharge hydrograph using effective rainfall and observed discharge hydrograph as input for five storm events.
Alternative methods include Genetic Algorithms (Goldberg 1989) and second-order derivative-based optimization algorithms such as Conjugate Gradient Descent, Quasi-Newton, Quick Propagation, Delta-Bar-Delta, and Levenberg Marquardt, which are fast and effective algorithms but may be subject to over-fitting (see Patterson 1996; Haykin 1994; Fausett 1994).
In conjunction with the NUFFT, the conjugate gradient descent algorithm of Lustig et al. [32] is then used to solve the optimization problem defined by: {widehat{x}}_{lambda }= arg kern0.2em mi{n}_{tilde{x}}kern1.5em left{{leftVert varPhi tilde{x}-brightVert}_{ell_2}^2kern1.75em +kern1.5em lambda {leftVert varPsi tilde{x}rightVert}_{ell_1}right} (3).
A two-stage process is used to train the network: 30 epochs of scaled conjugate gradient descent followed by Quasi-Newton BFGS optimisation for 100 epochs.
However, in general we can use non-linear optimization methods, such as conjugate gradient descent, to find a solution (in the worst case, the solution will be only a local minima).
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com