joe-lynch/numerical-optimisation

Numerical optimisation methods including the cauchy point, dogleg point, line search and steepest descent.

File Descriptions

dogleg.m

To run this function call dogleg(xn, fx, gx, H, H_, delta)
[although is called as part of tr_dogleg]

where

• xn : initial point
• fx : actual function
• gx : gradient function
• H : Hessian matrix
• H_ : inverse Hessian matrix
• delta : radius of the trust region

sr1.m

To run this function call sr1(H, H_, d, y, eta)
[although is called as part of tr_dogleg]

where

• H : Hessian matrix
• H_ : inverse Hessian matrix
• d : step between two points
• y : difference between gradient values
• eta : small value greater than zero

tr_dogleg.m

To run this function call tr_dogleg(f, df, H, H_, xn, delta, delmax, rho_ac, tol)

where

• f : actual function
• df : gradient function
• H : Hessian matrix
• H_ : inverse Hessian matrix
• xn : initial point
• delta : radius of the trust region
• delmax : maximum radius of the trust region
• rho_ac : accuracy
• tol : tolerance

Note that eta, is defined as 10^(-6) in the file tr_dogleg.m