In this paper, we introduce a new variant of the BFGS method designed to perform well when gradient measurements are corrupted by noise. We show that treating secant condition with penalty approach motivated regularized least squares estimation generates parametric family original update at one extreme and not updating inverse Hessian approximation other extreme. Furthermore, find curvature is ...

In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established under suitable conditions. The numerical results of the test problems show that ...

The relationship between variable-metric methods derived by norm minimization and those derived by symmetrization of rank-one updates for sparse systems is studied, and an analogue of Dennis's nonsparse symmetrization formula derived. A new method of using norm minimization to produce a sparse analogue of any nonsparse variable-metric method is proposed. The sparse BFGS generated by this method...

Issues of surfaces, e.g., inspired from beetle's back, spider silk, cactus stem, etc., become the active area of research on designing novel materials in need of human beings to acquire fresh water resource from air. However, the design of materials on surface structure is little achieved on controlling of micro-scale drop transport in a long distance. Here, we report the ability of micro-drop ...

The self-scaling quasi-Newton method solves an unconstrained optimization problem by scaling the Hessian approximation matrix before it is updated at each iteration to avoid the possible large eigenvalues in the Hessian approximation matrices of the objective function. It has been proved in the literature that this method has the global and superlinear convergence when the objective function is...

We present a class of methods which is a combination of the limited memory BFGS method and the truncated Newton method. Each member of the class is defined by the (possibly dynamic) number of vector pairs of the L-BFGS method and the forcing sequence of the truncated Newton method. We exemplify with a scheme which makes the hybrid method perform like the L-BFGS method far from the solution, and...

In previous work, the authors provided a foundation for the theory of variable metric proximal point algorithms in Hilbert space. In that work conditions are developed for global, linear, and super–linear convergence. This paper focuses attention on two matrix secant updating strategies for the finite dimensional case. These are the Broyden and BFGS updates. The BFGS update is considered for ap...

In this article, we explore the effectiveness of different numerical techniques in the training of backpropaqgation neural networks (BPNN) which are fed with wavelet-transformed data to capture useful information on various time scales. The purpose is to predict S&P500 future prices using BPNN trained with conjugate gradient (Fletcher-Reeves update, Polak-Ribiére update, Powell-Beale restart), ...

In this paper, we propose a hybrid Gauss-Newton structured BFGS method with a new update formula and a new switch criterion for the iterative matrix to solve nonlinear least squares problems. We approximate the second term in the Hessian by a positive definite BFGS matrix. Under suitable conditions, global convergence of the proposed method with a backtracking line search is established. Moreov...

This paper analyzes and improves the linearized Bregman method for solving the basis pursuit and related sparse optimization problems. The analysis shows that the linearized Bregman method has the exact regularization property; namely, it converges to an exact solution of the basis pursuit problem whenever its smooth parameter α is greater than a certain value. The analysis is based on showing ...