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This paper is concerned with the open problem whether BFGS method with inexact line search converges globally when applied to nonconvex uncon-strained optimization problems. We propose a cautious BFGS update and prove that the method with either Wolfe-type or Armijo-type line search converges globally if the function to be minimized has Lipschitz continuous(More)
Recently, Li et al. (Comput. Optim. Appl. 26:131–147, 2004) proposed a regularized Newton method for convex minimization problems. The method retains local quadratic convergence property without requirement of the singularity of the Hessian. In this paper, we develop a truncated regularized Newton method and show its global convergence. We also establish a(More)
This paper studies convergence properties of regularized Newton methods for minimizing a convex function whose Hessian matrix may be singular everywhere. We show that if the objective function is LC 2 , then the methods possess local quadratic convergence under a local error bound condition without the requirement of isolated nonsingular solutions. By using(More)
The mixed complementarity problem can be reformulated as a nonsmooth equation by using the median operator. In this paper, we rst study some useful properties of this refor-mulation and then derive the Chen-Harker-Kanzow-Smale smoothing function for the mixed complementarity problem. On the basis of this smoothing function, we present a smoothing Newton(More)