An efficient gradient method with approximately optimal stepsizes based on regularization models for unconstrained optimization

It is widely accepted that the stepsize of great significance to gradient method. An efficient method with approximately optimal stepsizes mainly based on regularization models proposed for unconstrained optimization. More specifically, if objective function not close a quadratic line segment between current and latest iterates, model exploited carefully generate stepsize. Otherwise, approximation used. In addition, when curvature non-positive, special developed. The convergence established under some weak conditions. Extensive numerical experiments indicated very promising. Due surprising efficiency, we believe methods can become strong candidates large-scale