Modified BFGS algorithm with particular descent condition for nonconvex functions

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.

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.

Electrical Resistance Tomography (ERT) is one of new methods for parameters measurement of two-phase flow. The image reconstruction algorithm is one of key parts of ERT system. Based on the optimization principle of BFGS algorithm (one kind of Quasi-Newton methods), a new image reconstruction algorithm of ERT for two-phase flow is proposed. To enable the acquirement of on-line measurement of two-phase flow, BFGS algorithm is modified to reduce computation and raise image reconstruction speed. The details are that the iteration direction is changed and the Hessian matrix of the objection function is replaced by the identity matrix. Experimental results show that the modified BFGS algorithm is stable and effective to reconstruct high quality image at fast speed.

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

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.

The manual examination of histological images like computed tomography (CT) images by physicians is prone to subjectivity and limited intra and inter-surgeon reproducibility, due to its heavy reliance on human interpretation. As result of which, diagnosis of cancer especially in lungs becomes less accurate and unreliable. So, a computer-aided diagnosis (CAD) system, based on artificial intelligence that efficiently detects nodules of any shape and size, is used for diagnosis without human intervention. In this work, we have developed a two stage CAD system in which the first stage involves pre-processing applied for a better quality image to enable higher success rate on detection following which the cancerous nodule region is segmented. The second stage involves artificial neural network (ANN) architecture which is trained using a modified BFGS algorithm. The proposed system was trained, tested, and evaluated specifically on the problem of detecting lung cancer nodules found on CT images to give a positive detection. A significant comparative analysis was done between the proposed method and several existing CAD systems used for lung nodule diagnosis and the proposed method using training-based neural networks prove to provide accuracy of 96.7% and also better specificity; thus, the overall performance of the CAD scheme was improved substantially.

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.

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.

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

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

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

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.

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...

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.