This paper studies an optimization problem for the unsteady partial differential equations (PDEs) with convection term, widely used in continuous casting process. Considering the change of casting speed, a dynamic opt...
详细信息
This paper studies an optimization problem for the unsteady partial differential equations (PDEs) with convection term, widely used in continuous casting process. Considering the change of casting speed, a dynamic optimization method based on new DY-HS hybrid conjugate gradient algorithm (DY-HSHCGA) is proposed. In the DY-HSHCGA, the Dai-Yuan and the Hestenes-Stiefel conjugategradientalgorithms are convex combined, and a new conjugate parameter theta k is obtained through the condition of quasi-Newton direction. Moreover, Lipschitz continuity of the gradient of cost function, as an important conditions for convergence, is analyzed in this paper. On the basis on this condition, the global convergence of DY-HSHCGA is proved. Finally, the effectiveness of DY-HSHCGA is verified by some instances from the steel plant. Comparing with other algorithms DY-HSHCGA obviously accelerates the convergence rate and reduces the number of iteration. The optimizer based on the DY-HSHCGA shows a more stable results.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
Billet production is for the most part completed in a continuous casting machine. To pro -duce a billet of suitable quality, the secondary cooling control system needs to provide an appropriate value of water flow rat...
详细信息
Billet production is for the most part completed in a continuous casting machine. To pro -duce a billet of suitable quality, the secondary cooling control system needs to provide an appropriate value of water flow rate. At present, most secondary cooling control methods are based on a heat transfer model for the billet, the accuracy of which can directly impact the cooling effect and further affect its quality. In practice, it is difficult to determine the heat flux at the billet's boundaries due to the complexity of continuous casting. Therefore, this study focuses on identifying the boundary conditions for the 3D heat transfer model of a billet with a linear coefficient. First, we transform the identification of boundary con-ditions into an optimization problem, prove the Lipschitz continuity of the cost function of the optimization problem, and obtain the Lipschitz constant. Second, based on the Lips-chitz continuity of the cost function, we present a modified hybridconjugategradient algo-rithm (MHCGA) to solve the optimization problem and then prove the global convergence of this MHCGA. Compared with other methods, the results of the simulation experiments clearly show that this MHCGA can reduce running time and iteration number. Third, to eliminate the ill-posedness of the inverse problem for identifying the boundary condition, we combined a regularization method with MHCGA. Simulation experiments confirmed that this method can effectively estimate the boundary conditions. Finally, the experimen-tal data from a steel plant verified the validity of our method, and the prediction results of the shell thickness were confirmed by the nail shooting method. (c) 2021 Published by Elsevier Inc.
Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybridconjugategradient methods for unconstrained optimization problems. Ou...
详细信息
Based on two modified secant equations proposed by Yuan, and Li and Fukushima, we extend the approach proposed by Andrei, and introduce two hybridconjugategradient methods for unconstrained optimization problems. Our methods are hybridizations of Hestenes-Stiefel and Dai-Yuan conjugategradient methods. Under proper conditions, we show that one of the proposed algorithms is globally convergent for uniformly convex functions and the other is globally convergent for general functions. To enhance the performance of the line search procedure, we propose a new approach for computing the initial value of the steplength for initiating the line search procedure. We give a comparison of the implementations of our algorithms with two efficiently representative hybridconjugategradient methods proposed by Andrei using unconstrained optimization test problems from the CUTEr collection. Numerical results show that, in the sense of the performance profile introduced by Dolan and Mor,, the proposed hybridalgorithms are competitive, and in some cases more efficient.
Fuzzy nonlinear equation (FNLE) plays an important role in many fields, including mathematics, engineering, statistics and so on. How to solve its numerical solution is an interesting problem. A hybridconjugate gradi...
详细信息
ISBN:
(纸本)9781424473281
Fuzzy nonlinear equation (FNLE) plays an important role in many fields, including mathematics, engineering, statistics and so on. How to solve its numerical solution is an interesting problem. A hybrid conjugate gradient algorithm (HCGA) was proposed for solving FNLE. First, the parametric form of the equation was translated into an equivalent unconstrained optimization problem (UOP). Then, HCGA was applied to solve the corresponding optimization problem. Convergence of the algorithm was proved. Finally, numerical examples were given to illustrate the efficencies of HCGA. The comparative study shows that HCGA for solving FNLE is superior to the existent steepest descent algorithm (SDA) in terms of convergence and the numbers of iteration.
暂无评论