The modified BFGS method with new secant relation ‎for unconstrained optimization problems‎

A Modified BFGS Algorithm for Unconstrained Optimization

In this paper we present a modified BFGS algorithm for unconstrained optimization. The BFGS algorithm updates an approximate Hessian which satisfies the most recent quasi-Newton equation. The quasi-Newton condition can be interpreted as the interpolation condition that the gradient value of the local quadratic model matches that of the objective function at the previous iterate. Our modified al...

A New Scaled Hybrid Modified BFGS Algorithms for Unconstrained Optimization

The BFGS methods is a method to solve an unconstrained optimization. Many modification have been done for solving this problems. In this paper, we present a new scaled hybrid modified BFGS. The new scaled hybrid modified BFGS algorithms are proposed and analyzed. The scaled hybrid modified BFGS can improve the number of iterations. Results obtained by the hybrid modified BFGS algorithms are com...

A modified secant method for unconstrained minimization

Modified Limited Memory Bfgs Method with Nonmonotone Line Search for Unconstrained Optimization

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

A modified nonmonotone BFGS algorithm for unconstrained optimization

In this paper, a modified BFGS algorithm is proposed for unconstrained optimization. The proposed algorithm has the following properties: (i) a nonmonotone line search technique is used to obtain the step size [Formula: see text] to improve the effectiveness of the algorithm; (ii) the algorithm possesses not only global convergence but also superlinear convergence for generally convex functions...

On the Global Convergence of the BFGS Method for Nonconvex Unconstrained Optimization Problems

This paper is concerned with the open problem whether BFGS method with inexact line search converges globally when applied to nonconvex unconstrained 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 gradients.