Module steihaug_cg

Steihaug conjugate-gradient trust region optimization.

This file is part of the minfx optimisation library at https://sourceforge.net/projects/minfx.

Classes

Steihaug

Functions

steihaug(func=None, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, epsilon=1e-08, delta_max=100000.0, delta0=1.0, eta=0.2, full_output=0, print_flag=0, print_prefix='')
Steihaug conjugate-gradient trust region algorithm.

Variables

__package__ = 'minfx'

Imports: dot, float64, sqrt, zeros, Min, Trust_region, Newton

Function Details

steihaug(func=None, dfunc=None, d2func=None, args=(), x0=None, func_tol=1e-25, grad_tol=None, maxiter=1000000.0, epsilon=1e-08, delta_max=100000.0, delta0=1.0, eta=0.2, full_output=0, print_flag=0, print_prefix='')

Steihaug conjugate-gradient trust region algorithm.

Page 75 from 'Numerical Optimization' by Jorge Nocedal and Stephen J. Wright, 1999, 2nd ed. The CG-Steihaug algorithm is:

• epsilon > 0
• p0 = 0, r0 = g, d0 = -r0
• if ||r0|| < epsilon:
  • return p = p0
• while 1:
  • if djT.B.dj <= 0:
    • Find tau such that p = pj + tau.dj minimises m(p) in (4.9) and satisfies ||p|| = delta
    • return p
  • aj = rjT.rj / djT.B.dj
  • pj+1 = pj + aj.dj
  • if ||pj+1|| >= delta:
    • Find tau such that p = pj + tau.dj satisfies ||p|| = delta
    • return p
  • rj+1 = rj + aj.B.dj
  • if ||rj+1|| < epsilon.||r0||:
    • return p = pj+1
  • bj+1 = rj+1T.rj+1 / rjT.rj
  • dj+1 = rj+1 + bj+1.dj