A New Modified Conjugate Gradient for Nonlinear Minimization Problems

Abstract

The conjugate gradient is a highly effective technique to solve the unconstrained nonlinear minimization problems and it is one of the most well-known methods. It has a lot of applications. For large-scale, unconstrained minimization problems, conjugate gradient techniques are widely applied. In this paper, we will suggest a new parameter of conjugate gradient to solve the nonlinear unconstrained minimization problems, based on parameter of Dai and Liao. We will study the property of the descent ,the property of the sufficient descent and property of the global convergence a new method. We introduce some numerical data to prove the efficacy of the our method.

Keywords

• Unconstrained Nonlinear minimization
• Method of Conjugate Gradient
• Descent property
• property of the Sufficient Descent and property of the Global convergence