A new family of conjugate gradient methods to solve unconstrained optimization problems

Abstract

A conjugate optimal coefficient is a crucial characteristic of conjugate gradient algorithms. The idea of accelerating the conjugate gradient by utilizing the conjugacy condition information and quadratic model. The gradient of the objective function is used to specify the search directions for traditional techniques. This work provides nonlinear conjugate gradient algorithms that primarily consider objective function information. One of the ways is as efficient as or more efficient than the conventional methods, according to numerical examples.

Subject Classification:

• Primary 93A30
• Secondary 49K15

Keywords:

• A new family of conjugate gradient methods
• Globally convergent
• Numerical results