In order to ameliorate convergence of the algorithm to invert the particle-size distribution (PSD) from laser diffraction data, an improved conjugate gradient algorithm (ICGA) is proposed. This method is independent o...
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In order to ameliorate convergence of the algorithm to invert the particle-size distribution (PSD) from laser diffraction data, an improved conjugate gradient algorithm (ICGA) is proposed. This method is independent of any given a priori information of the particle-size distribution. In the algorithm, each objective function is constructed according to an equation of the system of equations. Then iterations are carried out continuously between objective functions by choosing conjugategradient directions, and thus the objective functions are tied up. An iteration step-adjusting parameter is introduced, which depends on the row index vectors of the matrix equation. Two narrowly distributed particulate-certified reference materials, their mixture, and a widely distributed particle plate are used as samples to verify the algorithm. Experimental results show that the ICGA is sufficiently convergent and that the convergence points are stable. The presented method can be used to invert unimodal and multimodal PSD with high precision. (C) 2007 Society of Photo-Optical Instrumentation Engineers.
Each slab entering to the reheating furnace has an optimal and unique reheating curve. The process of obtaining the optimal reheating curve is to solve the typical Partial differential equations (PDE) constrained opti...
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Each slab entering to the reheating furnace has an optimal and unique reheating curve. The process of obtaining the optimal reheating curve is to solve the typical Partial differential equations (PDE) constrained optimization problem. Obviously, the solution of optimization problem is determined by both the precision of the mathematical PDE model and the numerical method. Firstly, the more accurate mathematical PDE model, in which some key parameters are reconsidered as temperature-dependent, is built for the reheating furnace. Secondly, the first-optimize-then-discretize approach is introduced to solve this PDE-constrained optimization problem. The analysis of the Frechet gradient of the cost functional is given and we can prove the gradient is Lipschitz continuous. Then, an improvedconjugategradient method is proposed to solve this problem. Finally, numerical simulations and experiment examples are given and analyzed. The results can prove the effectiveness of the proposed strategy.
In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standa...
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In this paper, we consider an optimal control problem of switched systems with input and state constraints. Since the complexity of such constraint and switching laws, it is difficult to solve the problem using standard optimization techniques. In addition, although conjugategradientalgorithms are very useful for solving nonlinear optimization problem, in practical implementations, the existing Wolfe condition may never be satisfied due to the existence of numerical errors. And the mode insertion technique only leads to suboptimal solutions, due to only certain mode insertions being considered. Thus, based on an improved conjugate gradient algorithm and a discrete filled function method, an improved bi-level algorithm is proposed to solve this optimization problem. Convergence results indicate that the proposed algorithm is globally convergent. Three numerical examples are solved to illustrate the proposed algorithm converges faster and yields a better cost function value than existing bi-level algorithms. (C) 2017 Elsevier Ltd. All rights reserved.
In this paper, the dual strategy is used to solve the 2-dimensional partial differential equation optimal control problem by introducing the adjoint problem approach to the optimization model. It is proved that the Fr...
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In this paper, the dual strategy is used to solve the 2-dimensional partial differential equation optimal control problem by introducing the adjoint problem approach to the optimization model. It is proved that the Frechet gradient of the cost functional could be written via the weak solution of the adjoint problem, and then, Lipschitz continuity of the gradient is derived. An improved conjugate gradient algorithm is used to solve this problem. Then, the proposed method is applied to obtain the reference values of the optimal furnace zone temperatures and achieve the desired temperature for steel slabs in the reheating furnace. Model validation and comparison between the mathematical model and the experiment results indicate that the present heat transfer model works well for the prediction of thermal behavior about the slab in the reheating furnace. Results of some computational experiments in the simulations of the A3 slab are illustrated, which verifies the effectiveness of the proposed method.
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