Modified BFGS Algorithm Research Articles

The global convergence of the BFGS method under a modified Yuan-Wei-Lu line search technique

This paper is focused on improving global convergence of the modified BFGS algorithm with Yuan-Wei-Lu line search formula. This improvement has been achieved by presenting a different line search approach and it is proved that the BFGS method with this line search converges globally if the function to be minimized has Lipschitz continuous gradients. The performance of the suggested algorithm is investigated via mathematical analysis and a simulation study.

A modified nonmonotone BFGS algorithm for unconstrained optimization

In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size alpha_{k} to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions; (iii) the algorithm produces better numerical results than those of the normal BFGS method.

采用简化Brown模型及改进BFGS法的相机自标定

采用简化Brown模型及改进BFGS法的相机自标定

A nonmonotone modified BFGS algorithm for nonconvex unconstrained optimization problems

In this paper, a modified BFGS algorithm is proposed to solve unconstrained optimization problems. First, based on a modified secant condition, an update formula is recommended to approximate Hessian matrix. Then thanks to the remarkable nonmonotone line search properties, an appropriate nonmonotone idea is employed. Under some mild conditions, the global convergence properties of the algorithm are established without convexity assumption on the objective function. Preliminary numerical experiments are also reported which indicate the promising behavior of the new algorithm.

Constrained optimal control of switched systems based on modified BFGS algorithm and filled function method

In this paper, we consider an optimal control problem of switched systems with a continuous-time inequality constraint. Because of the complexity of this constraint, it is difficult to solve this problem by standard optimization techniques. To overcome this difficulty, the problem is divided into a bi-level optimization problem involving a combination of a continuous-time optimal control problem and a discrete optimization problem. Then, a modified Broyden-Fletcher-Goldfarb-Shanno algorithm and a discrete filled function method is first proposed to solve this bi-level optimization problem. Finally, a numerical example is presented to illustrate the efficiency of our method.

New BFGS method for unconstrained optimization problem based on modified Armijo line search

In this article, a class of nonconvex unconstrained optimization problems is considered. As the Armijo line search is less costing in finding a steplength, a new Armijo-type line search (called WALS) with desirable features of the Wolfe condition is employed in the proposed modified BFGS method. A new updating formula incorporated with WALS is constructed and generates approximate Hessian matrices which are positive definite. On this basis, a class of well-defined modified BFGS algorithms is developed. It shows that under some suitable conditions, the modified BFGS algorithm is globally convergent. Numerical experiments are carried out on 20 benchmark test problems and the obtained results clearly indicate the effectiveness of the developed algorithm over two most popular BFGS-type algorithms available in the literature.

A modified BFGS algorithm based on a hybrid secant equation

By making a convex combination of the modified secant equations proposed by Yuan and Wei et al., a hybrid secant equation and also, a modified BFGS algorithm is proposed. The hybridization parameter is effectively computed using the available information of recent iterations. Under proper conditions, it is shown that the proposed algorithm is globally, locally and superlinearly convergent. By using the performance profile introduced by Dolan and More, a comparison between the implementations of the proposed algorithm and two efficient modified BFGS algorithms proposed by Yuan and Wei et al., on a set of unconstrained optimization test problems from the CUTEr collection, is done. Numerical results demonstrating the efficiency of the proposed modified BFGS algorithm are reported.

An Intelligent Neural Networks System for Adaptive Learning and Prediction of a Bioreactor Benchmark Process

Abstract The adaptive learning and prediction of a highly nonlinear and time-varying bioreactor benchmark process is studied using NeurOn-Line, a graphical tool kit for developing and deploying neural networks in the G2 real time intelligent environment, and a new modified Broyden, Fletcher, Goldfarb, and Shanno (BFGS) quasi-Newton algorithm. The modified BFGS algorithm for the adaptive learning of back propagation (BP) neural networks is developed and embedded into NeurOn-Line by introducing a new search method of learning rate to the full memory BFGS algorithm. Simulation results show that the adaptive learning and prediction neural network system can quickly track the time-varying and nonlinear behavior of the bioreactor.

Global convergence of a modified BFGS-type method for unconstrained non-convex minimization

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm associated with the general line search model. The idea of the algorithm is to modify the approxim...

Global convergence properties of two modified BFGS-type methods

This article studies a modified BFGS algorithm for solving smooth unconstrained strongly convex minimization problem. The modi- fied BFGS method is based on the new quasi-Newton equation Bk+1sk = yk where y k = yk + Aksk and Ak is a matrix. Wei, Li and Qi (WLQ) have proven that the average performance of two of those algorithms is better than that of the classical one. In this paper, we prove the global convergence of these algorithms associated to a general line search rule. where g(x) denotes the gradient of f at x and k·kdenotes the Euclidean norm of a vector. We abbreviate g(xk), f(xk )a sgk, fk, respectively. The quasi-Newton algorithm is a practical method for solving unconstrained convex programme from the computation point of view. The convergence properties of the BFGS method for convex minimization have been studied by many researchers. There have already been a lot of achievements in global convergence properties of BFGS algorithm. Powell (2) has proved the global convergence properties of

A type of modified BFGS algorithm with any rank defects and the local Q-superlinear convergence properties

A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper.The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.

Global convergence properties of the modified BFGS method associating with general line search model

To the unconstrained programme of non-convex function, this article give a modified BFGS algorithm. The idea of the algorithm is to modify the approximate Hessian matrix for obtaining the descent direction and guaranteeing the efficacious of the quasi-Newton iteration pattern. We prove the global convergence properties of the algorithm associating with the general form of line search, and prove the quadratic convergence rate of the algorithm under some conditions.

A Modified BFGS Algorithm for Unconstrained Optimization

Computing Centre, Academia Sinica, Beijing 100080, China[Received 25 April 1989 and in revised form 16 October 1990]In this paper we present a modified BFGS algorithm for unconstrainedoptimization. The BFGS algorithm updates an approximate Hessian whichsatisfies the most recent quasi-Newton equation. The quasi-Newton condition canbe interpreted as the interpolation condition that the gradient value of the localquadratic model matches that of the objective function at the previous iterate.Our modified algorithm requires that the function value is matched, instead of thegradient value, at the previous iterate. The modified algorithm preserves theglobal and local superlinear convergence properties of the BFGS algorithm.Numerical results are presented, which suggest that a slight improvement hasbeen achieved.1. Introduction