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Practical gradient and conjugate gradient methods on flag manifolds
Flag manifolds, sets of nested sequences of linear subspaces with fixed dimensions, are rising in numerical analysis and statistics. The current...
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Shape Optimization with Nonlinear Conjugate Gradient Methods
In this chapter, we investigate recently proposed nonlinear conjugate gradient (NCG) methods for shape optimization problems. We briefly introduce...
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Conjugate Gradient Methods
These methods are characterized by very strong convergence properties and modest storage requirements. They are dedicated to solving large-scale...
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Spectral conjugate gradient methods for vector optimization problems
In this work, we present an extension of the spectral conjugate gradient (SCG) methods for solving unconstrained vector optimization problems, with...
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Conjugate Direction Methods
We consider conjugate direction methods, Conjugate direction method a class of algorithms originally introduced as iterative methods for solving...
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Multiobjective Conjugate Gradient Methods on Riemannian Manifolds
In this paper, we present the multiobjective optimization methods of conjugate gradient on Riemannian manifolds. The concepts of optimality and Wolfe...
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Some improved Dai–Yuan conjugate gradient methods for large-scale unconstrained optimization problems
In this paper, we introduce some modifications of the classic conjugate gradient method Dai–Yuan, to solve large-scale unconstrained optimization...
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Nonlinear conjugate gradient for smooth convex functions
The method of nonlinear conjugate gradients (NCG) is widely used in practice for unconstrained optimization, but it satisfies weak complexity bounds...
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Riemannian conjugate gradient methods for computing the extreme eigenvalues of symmetric tensors
In this paper, we propose two kinds of Riemannian conjugate gradient methods for computing the extreme eigenvalues of even order symmetric tensors....
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Practical Restrictively Preconditioned Conjugate Gradient Methods for a Class of Block Two-by-Two Linear Systems
We further analyze the solution of a class of block two-by-two linear systems. Instead of using the preconditioned GMRES iteration methods, we...
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A modified Fletcher-Reeves conjugate gradient method for unconstrained optimization with applications in image restoration
The Fletcher-Reeves (FR) method is widely recognized for its drawbacks, such as generating unfavorable directions and taking small steps, which can...
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A limited memory subspace minimization conjugate gradient algorithm for unconstrained optimization
Subspace minimization conjugate gradient (SMCG) methods are a class of quite efficient iterative methods for unconstrained optimization. The...
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Two classes of spectral conjugate gradient methods for unconstrained optimizations
The spectral conjugate gradient method is effective iteration method for solving large-scale unconstrained optimizations. In this paper, using the...
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Two spectral conjugate gradient methods for unconstrained optimization problems
Two new spectral conjugate gradient methods (ZL1 method and ZL2 method) for solving unconstrained optimization problems are established. Under the...
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A Nonlinear Conjugate Gradient Method Using Inexact First-Order Information
Conjugate gradient methods are widely used for solving nonlinear optimization problems. In some practical problems, we can only get approximate...
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Alternative extension of the Hager–Zhang conjugate gradient method for vector optimization
Recently, Gonçalves and Prudente proposed an extension of the Hager–Zhang nonlinear conjugate gradient method for vector optimization (Comput Optim...
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Riemannian conjugate gradient method for low-rank tensor completion
Tensor completion aims to reconstruct a high-dimensional data from the partial element missing tensors under a low-rank constraint, which may be seen...
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A New Subspace Minimization Conjugate Gradient Method for Unconstrained Minimization
Subspace minimization conjugate gradient (SMCG) methods are a class of quite efficient iterative methods for unconstrained optimization and have...
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A three-term conjugate gradient descent method with some applications
The stationary point of optimization problems can be obtained via conjugate gradient (CG) methods without the second derivative. Many researchers...
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A conjugate gradient projection method with restart procedure for solving constraint equations and image restorations
The conjugate gradient projection method is one of the most effective methods for solving large-scale nonlinear monotone convex constrained...
