scholarly journals The spectral conjugate gradient method in variational adjoint assimilation for model terrain correction I: Theoretical frame

Author(s):  
Sulin Tao ◽  
Yuhong Li ◽  
Isaac Mugume ◽  
Shuanghe Shen
2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Liu Jinkui ◽  
Du Xianglin ◽  
Wang Kairong

A mixed spectral CD-DY conjugate descent method for solving unconstrained optimization problems is proposed, which combines the advantages of the spectral conjugate gradient method, the CD method, and the DY method. Under the Wolfe line search, the proposed method can generate a descent direction in each iteration, and the global convergence property can be also guaranteed. Numerical results show that the new method is efficient and stationary compared to the CD (Fletcher 1987) method, the DY (Dai and Yuan 1999) method, and the SFR (Du and Chen 2008) method; so it can be widely used in scientific computation.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
ShiChun Lv ◽  
Shou-Qiang Du

<p style='text-indent:20px;'>In recent years, the tensor complementarity problem has attracted widespread attention and has been extensively studied. The research work of tensor complementarity problem mainly focused on theory, solution methods and applications. In this paper, we study the solution method of tensor complementarity problem. Based on the equivalence relation of the tensor complementarity problem and unconstrained optimization problem, we propose a new smoothing spectral conjugate gradient method with Armijo line search. Under mild conditions, we establish the global convergence of the proposed method. Finally, some numerical results are given to show the effectiveness of the proposed method and verify our theoretical results.</p>


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