A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose...A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum.展开更多
The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization p...The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.展开更多
Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summa...Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summarize the rough line rule of the penalty parameter and kernel width, and propose a novel linear search method to obtain these two optimal parameters. We use a direct-setting method with thresholds to set the epsilon parameter of SVR. The proposed method directly locates the right search field, which greatly saves computing time and achieves a stable, high accuracy. The method is more competitive for both SVC and SVR. It is easy to use and feasible for a new data set without any adjustments, since it requires no parameters to set.展开更多
A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Eac...A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Each of the searchers moves continuously along his line in both directions of his starting point. When the target is valuable as a person lost on one of disjoint roads, or is serious as a car filled with explosives which moves randomly in one of disjoint roads, in these cases the search effort must be unrestricted and then we can use more than one searcher. In this paper we show the existence of a search plan such that the expected value of the first meeting time between the target and one of the two searchers is minimum.展开更多
In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their s...In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their search from the origin on the first line and other two searchers begin their search from the origin on the second line. But the motion of the two searchers on the first line is independent from the motion of the other two searchers on the second line. Here we introduce a model of search plan and investigate the expected value of the first meeting time between one of the searchers and the lost target. Also, we prove the existence of a search plan which minimizes the expected value of the first meeting time between one of the searchers and the target.展开更多
It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, thi...It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
文摘A target is assumed to move according to a Brownian motion on the real line. The searcher starts from the origin and moves in the two directions from the starting point. The object is to detect the target. The purpose of this paper is to find the conditions under which the expected value of the first meeting time of the searcher and the target is finite, and to show the existence of a search plan which made this expected value minimum.
文摘The essence of the linear search is one-dimension nonlinear minimization problem, which is an important part of the multi-nonlinear optimization, it will be spend the most of operation count for solving optimization problem. To improve the efficiency, we set about from quadratic interpolation, combine the advantage of the quadratic convergence rate of Newton's method and adopt the idea of Anderson-Bjorck extrapolation, then we present a rapidly convergence algorithm and give its corresponding convergence conclusions. Finally we did the numerical experiments with the some well-known test functions for optimization and the application test of the ANN learning examples. The experiment results showed the validity of the algorithm.
基金supported by the National Basic Research Program (973) of China (No. 2009CB724006)the National Natural Science Foun-dation of China (No. 60977010)
文摘Selecting the optimal parameters for support vector machine (SVM) has long been a hot research topic. Aiming for support vector classification/regression (SVC/SVR) with the radial basis function (RBF) kernel, we summarize the rough line rule of the penalty parameter and kernel width, and propose a novel linear search method to obtain these two optimal parameters. We use a direct-setting method with thresholds to set the epsilon parameter of SVR. The proposed method directly locates the right search field, which greatly saves computing time and achieves a stable, high accuracy. The method is more competitive for both SVC and SVR. It is easy to use and feasible for a new data set without any adjustments, since it requires no parameters to set.
文摘A target is assumed to move randomly on one of two disjoint lines L1 and L2 according to a stochastic process . We have two searchers start looking for the lost target from some points on the two lines separately. Each of the searchers moves continuously along his line in both directions of his starting point. When the target is valuable as a person lost on one of disjoint roads, or is serious as a car filled with explosives which moves randomly in one of disjoint roads, in these cases the search effort must be unrestricted and then we can use more than one searcher. In this paper we show the existence of a search plan such that the expected value of the first meeting time between the target and one of the two searchers is minimum.
文摘In this paper, we study the quasi-coordinated search technique for a lost target assumed to move randomly on one of two disjoint lines according to a random walk motion, where there are two searchers beginning their search from the origin on the first line and other two searchers begin their search from the origin on the second line. But the motion of the two searchers on the first line is independent from the motion of the other two searchers on the second line. Here we introduce a model of search plan and investigate the expected value of the first meeting time between one of the searchers and the lost target. Also, we prove the existence of a search plan which minimizes the expected value of the first meeting time between one of the searchers and the target.
文摘It is well known that the line search methods play a very important role for optimization problems. In this paper a new line search method is proposed for solving unconstrained optimization. Under weak conditions, this method possesses global convergence and R-linear convergence for nonconvex function and convex function, respectively. Moreover, the given search direction has sufficiently descent property and belongs to a trust region without carrying out any line search rule. Numerical results show that the new method is effective.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
