Modified nonlinear conjugate gradient method with sufficient descent condition for unconstrained optimization
Jinkui Liu,Shaoheng Wang +1 more
TL;DR: Numerical results show that the modified method is efficient and stationary by comparing with the well-known Polak-Ribiére-Polyak method, CG-DESCENT method and DSP-CG method using the unconstrained optimization problems from More and Garbow.
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Abstract: In this paper, an efficient modified nonlinear conjugate gradient method for solving unconstrained optimization problems is proposed. An attractive property of the modified method is that the generated direction in each step is always descending without any line search. The global convergence result of the modified method is established under the general Wolfe line search condition. Numerical results show that the modified method is efficient and stationary by comparing with the wellknown Polak-Ribiere-Polyak method, CG-DESCENT method and DSP-CG method using the unconstrained optimization problems from More and Garbow (ACM Trans Math Softw 7, 17-41, 1981), so it can be widely used in scientific computation. Mathematics Subject Classification (2010) 90C26 · 65H10
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Citations
Enhanced Dai–Liao conjugate gradient methods for systems of monotone nonlinear equations
Mohammed Yusuf Waziri,Kabiru Ahmed,Jamilu Sabi’u,Abubakar Sani Halilu +3 more
- 01 Mar 2021
TL;DR: In this article, two conjugate gradient methods for solving large-scale monotone nonlinear equations were proposed by combining the hyperplane projection method by Solodov and Svaiter (Reformulation: nonsmooth, piecewise smooth, semismooth and smoothing methods).
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Descent Perry conjugate gradient methods for systems of monotone nonlinear equations
TL;DR: A family of Perry conjugate gradient methods for solving large-scale systems of monotone nonlinear equations is presented, showing that the proposed methods are promising and more effective compared to some existing methods in the literature.
28
Symmetric Perry conjugate gradient method
Dongyi Liu,Genqi Xu +1 more
TL;DR: A family of new conjugate gradient methods is proposed based on Perry’s idea, which satisfies the descent property or the sufficient descent property for any line search, and the preliminary numerical comparisons show that these new algorithms are very effective algorithms for the large-scale unconstrained optimization problems.
A hybridization of the Hestenes-Stiefel and Dai-Yuan Conjugate Gradient Methods
TL;DR: The improved hybrid conjugate gradient technique as mentioned in this paper is a convex combination of the Dai-Yuan and Hestenes-Stiefel methodologies, which is used for unconstrained optimization.
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