Based on some new interpolation conditions, a quadratic interpolation model is constructed to approximate the objective function, and then a class of modified BFGS methods with function value information is presented. The new methods satisfy some new weak secant equations and there is a...

A simple and implementable two-loop smoothing method for semi-infinite minimax problem is given with the discretization parameter and the smoothing parameter being updated adaptively. We prove the global convergence of the algorithm when the steepest descent method or a BFGS type quasi-Newton...

In this paper, a modified non-monotone BFGS (MNBFGS) method for non-convex unconstrained optimization is proposed. Under some mild conditions, the global convergence of the given method is established, when the objective function is non-convex. Preliminary numerical comparisons, which show the...

An active set limited memory BFGS algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction is determined by a lower dimensional system of linear equations in free subspace. The implementations of the...

An active set limited memory BFGS algorithm for large-scale bound constrained optimization is proposed. The active sets are estimated by an identification technique. The search direction is determined by a lower dimensional system of linear equations in free subspace. The implementations of the...