Speaker: Pro.Yuhong Dai (Chinese Academy of Sciences)

Title:Steepest Descent Methods Revisited

Time: Sat, Nov.17, 2018 , AM:10:45-11:45

Location: Room 4135, Building No.4, Wushan Campus

Abstract：  

The steepest decent method plays a special role in the development of nonlinear optimization and numerical analysis. The classical steepest decent method, which was dated back to Cauchy (1847), keeps a monotone decrease in the objective function at each iteration, but performs very slow even when the problem is ill-conditioning and possesses the notorious zigzagging phenomenon. By imposing a certain quasi-Newton property, Barzilai and Borwein (1988) proposed a novel gradient method, which has a heavy non-monotone behavior in the objective function, but greatly improves the numerical efficiency. In this talk, we shall revisit both monotone and non-monotone steepest descent methods and point out some possible research problems.