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The Dai-Liao nonlinear conjugate gradient method with optimal parameter choices
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A descent family of Dai–Liao conjugate gradient methods
TLDR
It is shown that the methods of the suggested class of Dai–Liao conjugate gradient methods are globally convergent for uniformly convex objective functions.
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Two new conjugate gradient methods based on modified secant equations
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Two hybrid nonlinear conjugate gradient methods based on a modified secant equation
TLDR
Two hybridizations of the Hestenes–Stiefel and Dai–Yuan conjugate gradient methods are suggested based on Andrei's approach of hybridizing the CG parameters convexly and Powell’s approach of nonnegative restriction of theCG parameters.
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A modified BFGS algorithm based on a hybrid secant equation
TLDR
Under proper conditions, it is shown that the proposed algorithm is globally, locally and superlinearly convergent.
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A class of adaptive Dai–Liao conjugate gradient methods based on the scaled memoryless BFGS update
TLDR
Preliminary numerical results demonstrate a proper choice for the parameter of the proposed class of conjugate gradient methods may lead to promising numerical performance.
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An extended three-term conjugate gradient method with sufficient descent property
. An extension of the three-term conjugate gradient method proposed by Zhang et al. is suggested. Based on an eigenvalue analysis on the search direction matrix, it is shown that the method possesses…
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A descent extension of the Polak-Ribière-Polyak conjugate gradient method
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Two modified three-term conjugate gradient methods with sufficient descent property
TLDR
Two nonlinear conjugates gradient methods are proposed, making modifications on the conjugate gradient methods proposed by Dai and Liao (Appl Math Optim 43:87–101, 2001), and Zhou and Zhang (Optim Methods Softw 21:707–714, 2006).
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A modified scaled memoryless BFGS preconditioned conjugate gradient method for unconstrained optimization
TLDR
Numerical comparisons of the implementations of the proposed modified scaled conjugate gradient method made on a set of unconstrained optimization test problems of the CUTEr collection show the efficiency of the implemented method in the sense of the performance profile introduced by Dolan and Moré.
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