In this chapter first-order unconstrained optimization approaches have been discussed. These approaches assume the existence of first-order derivatives either through a finite difference approximation or through an adjoint sensitivity approach and also the steepest descent approach and conjugate gradient approaches have been discussed.

Chapter Contents:

• 6.1 Introduction
• 6.2 The steepest descent method
• 6.3 The conjugate directions method
• 6.3.1 Definition of conjugacy
• 6.3.2 Powell's method of conjugate directions
• 6.4 Conjugate gradient methods
• A6.1 Solution of large systems of linear equations
• A6.2 The design of digital FIR filters
• References
• Problems

Inspec keywords: conjugate gradient methods; optimisation; approximation theory

Other keywords: conjugate gradient approaches; adjoint sensitivity approach; first-order unconstrained optimization approaches; finite difference approximation; steepest descent approach

Subjects: Optimisation techniques; Optimisation; Optimisation techniques; Numerical analysis; Interpolation and function approximation (numerical analysis); Interpolation and function approximation (numerical analysis)