Abstract
A New Globally Convergent Self-Scaling Vm Algorithm for Convex and Nonconvex Optimization
Highlights
Consider the unconstrained optimization problem: min f (x) x Rn ...(1)Where f is a continuously differentiable function of n variables .Quasi-Newton methods for solving (1) often needs the new search direction dk 1 at each iteration given by: dk Hk gk ...( 2)Where gk 1 f the gradient of is f evaluated at the current iteration xk 1 (Storey & HU., 1993)
We have proposed a new self-scaling VM-type for unconstrained minimization based on a modified Quasi-Newton condition
We claim that the formula (26) - (27) will be more efficient and better than the standard Broyden - Fletcher-Goldfarb - Shanno (BFGS)
Summary
Consider the unconstrained optimization problem: min f (x) x Rn ...(1). Where f is a continuously differentiable function of n variables .Quasi-. Newton methods for solving (1) often needs the new search direction dk 1 at each iteration given by: dk Hk gk ...( 2). Where gk 1 f (xk 1) the gradient of is f evaluated at the current iteration xk 1 (Storey & HU., 1993). One computes the iteration by the formula xk 1 xk k d k ...(3). Where the step size k satisfies the Wolfe – conditions f (xk kdk ) f (xk ) k d
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