In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best ite...In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.展开更多
A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized fle...A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.展开更多
Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented...Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.展开更多
In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization pro...In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization problem (COP), a class of nonmonotone trust region algorithmsis proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms isproved. In sec. 3, some results about the Cauchy point are provided. The展开更多
In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region al...In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model展开更多
文摘In this paper, we present a new line search and trust region algorithm for unconstrained optimization problems. The trust region center locates at somewhere in the negative gradient direction with the current best iterative point being on the boundary. By doing these, the trust region subproblems are constructed at a new way different with the traditional ones. Then, we test the efficiency of the new line search and trust region algorithm on some standard benchmarking. The computational results reveal that, for most test problems, the number of function and gradient calculations are reduced significantly.
文摘A generalized flexibility–based objective function utilized for structure damage identification is constructed for solving the constrained nonlinear least squares optimized problem. To begin with, the generalized flexibility matrix (GFM) proposed to solve the damage identification problem is recalled and a modal expansion method is introduced. Next, the objective function for iterative optimization process based on the GFM is formulated, and the Trust-Region algorithm is utilized to obtain the solution of the optimization problem for multiple damage cases. And then for computing the objective function gradient, the sensitivity analysis regarding design variables is derived. In addition, due to the spatial incompleteness, the influence of stiffness reduction and incomplete modal measurement data is discussed by means of two numerical examples with several damage cases. Finally, based on the computational results, it is evident that the presented approach provides good validity and reliability for the large and complicated engineering structures.
基金Research partially supported by the Faculty Research Grant RIG-35547 and ROG-34628 of the University of North Texas and in part by the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation with ad
文摘Presents information on a study which analyzed an interior trust-region-based algorithm for linearly constrained minimization problems. Optimality conditions for the linearly constrained minimization problem presented; Vectors for each updating step in the algorithm proposed; Establishment of the convergence properties of the proposed algorithm.
基金Project supported by the National Natural Science Foundation of China and Postdoctoral Foundation of China.
文摘In this note, we consider the following constrained optimization problem (COP) min f(x), x∈Ωwhere f(x): R^n→R is a continuously differentiable function on a closed convex set Ω. Forthe constrained optimization problem (COP), a class of nonmonotone trust region algorithmsis proposed in sec. 1. In sec. 2, the global convergence of this class of algorithms isproved. In sec. 3, some results about the Cauchy point are provided. The
文摘In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model
