A New super-memory gradient method with curve search rule for unconstrained minimization problems

作者：Tang, Jingyong^*; Dong, Li; Zhou, Jinchuan

来源：International Journal of Applied Mathematics and Statistics, 2013, 31(1): 85-95.

• Curve search
• Curve search rule
• Global convergence
• Linear convergence rate
• Multi-step
• Numerical results
• Search direction
• Step size
• Unconstrained minimization problem

In this paper we present a new super-memory gradient method for unconstrained minimization problems. The global convergence and linear convergence rate of this method are proved under some mild conditions. The method uses previous multi-step iterative information and a curve search rule to generate new iterative points. It is particular that the search direction and the step-size are determined simultaneously at each iteration. This makes the new method converge more stably than other similar methods and be suitable for solving large scale unconstrained minimization problems. Numerical results show that our method is effective in practical computation.

• 出版日期2013
• 单位上海交通大学; 山东大学