A new adaptive Barzilai and Borwein method for unconstrained optimization

作者：Liu, Hongwei; Liu, Zexian^*; Dong, Xiaoliang

来源：Optimization Letters, 2018, 12(4): 845-873.

DOI：10.1007/s11590-017-1150-9

• Barzilai and Borwein (BB) method
• Adaptive stepsize
• Nonmonotone line search
• Broyden class update formula
• Strictly convex quadratic minimization

In this paper we view the Barzilai and Borwein (BB) method from a new angle, and present a new adaptive Barzilai and Borwein (NABB) method with a nonmonotone line search for general unconstrained optimization. In the proposed method, the scalar approximation to the Hessian matrix is updated by the Broyden class formula to generate an adaptive stepsize. It is remarkable that the new stepsize is chosen adaptively in the interval which contains the two well-known BB stepsizes. Moreover, for the negative curvature direction, a strategy for the choice of the stepsize is designed to accelerate the convergence rate of the NABB method. Furthermore, we apply the NABB method without any line search to strictly convex quadratic minimization. The numerical experiments show the NABB method is very promising.

• 出版日期2018-6
• 单位北方民族大学; 贺州学院; 西安电子科技大学