6 Quasi-Newton Methods

• 6.1 The BFGS Method
  • Properties of The BFGS Method
  • implementation
• 6.2 The SR1 Method
  • Properties of SR1 updating
• 6.3 The Broyden Class
• 6.4 Convergence Analysis
  • Global Convergence of The BFGS Method
  • Superliner Convergence of the BFGS Method
  • Convergence Analysis of the SR1 Method

Quasi-Newton methods require only the gradient of the objective function at each iterate. By measuring the changes in gradient, they construct a model of the objective function that is good enough to produce superlinear convergence.