The global convergence of the BFGS method with a modified WWP line search for nonconvex functions

Numerical Algorithms - The BFGS method, which has great numerical stability, is one of the quasi-Newton line search methods. However, the global convergence of the BFGS method with a Wolfe line...     

BFGS trust-region method for symmetric nonlinear equations

In this paper, we propose a BFGS trust-region method for solving symmetric nonlinear equations. The global convergence and the superlinear convergence of the presented method will be established under favorable conditions. Numerical results show that the new algorithm is effective.     

An active set limited memory BFGS algorithm for bound constrained optimization

In this paper, an active set limited BFGS algorithm is proposed for bound constrained optimization. The global convergence will be established under some suitable conditions. Numerical results show that the given method is effective.     

Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization

By means of a gradient strategy, the Moreau-Yosida regularization, limited memory BFGS update, and proximal method, we propose a trust-region method for nonsmooth convex minimization. The search direction is the combination of the gradient direction and the trust-region direction. The global convergence of this method is established under suitable conditions. Numerical results show that this method is competitive to other two methods.     

A Trust Region Algorithm with Conjugate Gradient Technique for Optimization Problems

By means of a conjugate gradient strategy, we propose a trust region method for unconstrained optimization problems. The search direction is an adequate combination of the conjugate gradient direction and the trust-region direction. The global convergence and the quadratic convergence of this method are established under suitable conditions. Numerical results show that the presented method is competitive to the trust region method and the conjugate gradient method.     

An effective adaptive trust region algorithm for nonsmooth minimization

In this paper, an adaptive trust region algorithm that uses Moreau–Yosida regularization is proposed for solving nonsmooth unconstrained optimization problems. The proposed algorithm combines a modified secant equation with the BFGS update formula and an adaptive trust region radius, and the new trust region radius utilizes not only the function information but also the gradient information. The global convergence and the local superlinear convergence of the proposed algorithm are proven under suitable conditions. Finally, the preliminary results from comparing the proposed algorithm with some existing algorithms using numerical experiments reveal that the proposed algorithm is quite promising for solving nonsmooth unconstrained optimization problems.     

A new adaptive trust region algorithm for optimization problems

It is well known that trust region methods are very effective for optimization problems. In this article, a new adaptive trust region method is presented for solving unconstrained optimization problems. The proposed method combines a modified secant equation with the BFGS updated formula and an adaptive trust region radius, where the new trust region radius makes use of not only the function information but also the gradient information. Under suitable conditions, global convergence is proved, and we demonstrate the local superlinear convergence of the proposed method. The numerical results indicate that the proposed method is very efficient.     

Adaptive three-term PRP algorithms without gradient Lipschitz continuity condition for nonconvex functions

Numerical Algorithms - We construct new polynomial interpolation schemes of Taylor and Hermite types in $\mathbb {R}^{n}$ . The interpolation conditions are real parts and imaginary parts of...     

在滴瓶上制作永久性标签

滴瓶作为盛贮液体试剂的仪器,在各学科的实验室、化验室和研究室里用得很普遍。长期以来,滴瓶一直是用纸制标签。纸制标签虽有一定的优点,但经常被试剂污染或腐蚀,致使字迹模糊。另外,擦洗滴瓶时,往往将标签纸弄脏或弄坏,以致更换标签,给实验工作人员带来很多麻烦。为此,我们试图在滴瓶上制作一种免除上述缺陷的永久性标签。通过实验,获得较好效果。