Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method t...
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Systems of nonlinear equations are ubiquitous in engineering, physics and mechanics, and have myriad applications. Generally, they are very difficult to solve. In this paper, we will present a filled function method to solve nonlinear systems. We will first convert the nonlinear systems into equivalent global optimization problems with the property: x* is a global minimizer if and only if its function value is zero. A filled function method is proposed to solve the converted global optimization problem. Numerical examples are presented to illustrate our new techniques. (C) 2010 Elsevier B.V. All rights reserved.
This paper considers a discrete-time optimal control problem subject to terminal state constraints and all-time-step inequality constraints, where the cost function involves a terminal cost, a summation cost and a pen...
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This paper considers a discrete-time optimal control problem subject to terminal state constraints and all-time-step inequality constraints, where the cost function involves a terminal cost, a summation cost and a penalty on the change of the control action. The variation of the control signal and the all-time-step constraints are non-smooth functions. Thus, this optimal control problem is formulated as a non-smooth constrained optimization problem. However, it is nonconvex and hence it may have many local minimum points. Thus, a filled function method is introduced in conjunction with local optimization techniques to solve this non-smooth and nonconvex constrained optimization problem. For illustration, two numerical examples are presented and solved using the proposed approach. (C) 2017 Elsevier B.V. All rights reserved.
A novel filledfunction with one parameter is suggested in this paper for finding a global minimizer for a general class of nonlinear programming problems with a closed bounded box. A new algorithm is presented accord...
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A novel filledfunction with one parameter is suggested in this paper for finding a global minimizer for a general class of nonlinear programming problems with a closed bounded box. A new algorithm is presented according to the theoretical analysis. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. (C) 2006 Elsevier B.V. All rights reserved.
In this paper, we develop a new filled function method to solve nonlinear integer programming problem. It is shown that any local minimizer of the new filledfunction constructed from a current local minimizer is eith...
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In this paper, we develop a new filled function method to solve nonlinear integer programming problem. It is shown that any local minimizer of the new filledfunction constructed from a current local minimizer is either a better local minimizer of the original integer programming problem or a vertex of its constrained domain. Hence a better local minimizer can be obtained just by local search scheme for the new filledfunction. An algorithm based on the nice properties of the new filledfunction is proposed for locating the global minimizer of the original integer programming problem. Several numerical examples are presented to show the efficiency of the algorithm. (c) 2005 Elsevier Inc. All rights reserved.
The filled function method is an efficient approach for finding a global minimizer of global optimization problems. The key of this kind of methods is the design of filledfunction. In this paper, we propose a new fil...
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The filled function method is an efficient approach for finding a global minimizer of global optimization problems. The key of this kind of methods is the design of filledfunction. In this paper, we propose a new filledfunction with one parameter that is continuously differentiable and always contains local information of objective function. Then, a new filled function method involved the proposed filledfunction for unconstrained global optimization problems is developed. Furthermore, numerical experiments are conducted to demonstrate the efficiency and reliability of our algorithm. We finally apply the proposed algorithm to study the pathological factors in renal cell carcinoma metastasis.
A new definition of the filledfunction is presented in this paper. Based on the definition, a new filledfunction is presented, and a global optimization algorithm is developed. The implementation of the algorithm on...
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A new definition of the filledfunction is presented in this paper. Based on the definition, a new filledfunction is presented, and a global optimization algorithm is developed. The implementation of the algorithm on several test problems is reported with satisfactory numerical results. The numerical experiments further show that the algorithm may solve higher dimensional global optimization problems. (C) 2015 Elsevier Inc. All rights reserved.
In this paper, a new global optimization approach based on the filled function method is proposed for solving box-constrained systems of nonlinear equations. We first convert the nonlinear system into an equivalent gl...
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In this paper, a new global optimization approach based on the filled function method is proposed for solving box-constrained systems of nonlinear equations. We first convert the nonlinear system into an equivalent global optimization problem, and then propose a new filled function method to solve the converted global optimization problem. Several numerical examples are presented and solved by using different local minimization methods, which illustrate the efficiency of the present approach. (c) 2009 Elsevier Inc. All rights reserved.
In this paper, we propose a new filled function method for finding a global minimizer of global optimization with inequality constraints. The proposed filledfunction is a continuously differentiable function with onl...
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In this paper, we propose a new filled function method for finding a global minimizer of global optimization with inequality constraints. The proposed filledfunction is a continuously differentiable function with only one parameter. Then, we can use classical local optimization methods to find a better minimizer of the proposed filledfunction with a few parameter adjustment. The numerical experiments are made and the results show that the proposed filled function method is effective.
In this paper, a filled function method for solving constrained global optimization problems is proposed. A filledfunction is proposed for escaping the current local minimizer of a constrained global optimization pro...
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In this paper, a filled function method for solving constrained global optimization problems is proposed. A filledfunction is proposed for escaping the current local minimizer of a constrained global optimization problem by combining the idea of filledfunction in unconstrained global optimization and the idea of penalty function in constrained optimization. Then a filled function method for obtaining a global minimizer or an approximate global minimizer of the constrained global optimization problem is presented. Some numerical results demonstrate the efficiency of this global optimization method for solving constrained global optimization problems.
In this paper, a new auxiliary function with one parameter on box constrained for escaping the current local minimizer of global optimization problem is proposed. First, a new definition of the filledfunction for box...
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In this paper, a new auxiliary function with one parameter on box constrained for escaping the current local minimizer of global optimization problem is proposed. First, a new definition of the filledfunction for box constrained minimization problem is given and under mild assumptions, this new auxiliary function is really a filledfunction. Then a new solution algorithm is proposed according to the theoretical analysis. And some numerical results demonstrate the efficiency of this method for box constrained global optimization. (c) 2007 Elsevier Inc. All rights reserved.
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