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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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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 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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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...
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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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An accelerated conjugate gradient method with adaptive two-parameter with applications in image restoration
This paper proposes an adaptive two-parameter accelerated conjugate gradient method, which satisfies the sufficient descent condition in the search...
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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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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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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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An inertial Fletcher–Reeves-type conjugate gradient projection-based method and its spectral extension for constrained nonlinear equations
In this paper, we initially enhance the Fletcher–Reeves (FR) conjugate parameter through a shrinkage multiplier, leading to a derivative-free...
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An improved spectral conjugate gradient projection method for monotone nonlinear equations with application
In this paper, we propose an enhanced spectral conjugate gradient (CG) projection method for solving monotone nonlinear equations with application in...
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A family of accelerated hybrid conjugate gradient method for unconstrained optimization and image restoration
In this paper, a family of hybrid conjugate parameters with restart procedure is proposed. In which, we design a hybrid conjugate parameter by using...
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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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Mixed-precision conjugate gradient algorithm using the groupwise update strategy
The conjugate gradient (CG) method is the most basic iterative solver for large sparse symmetric positive definite linear systems. In finite...
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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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A new subspace minimization conjugate gradient method based on conic model for large-scale unconstrained optimization
Conjugate gradient method is one of the most efficient methods for large-scale unconstrained optimization and has attracted focused attention of...
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Gradient Method
In this chapter we introduce the gradient method, which is one of the first methods proposed for the unconstrained minimization of differentiable...