Abstract
We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.
Highlights
Due to their simplicity and their low memory requirement, the conjugate gradient methods play a very important role for solving unconstrained optimization problems, especially for the large-scale optimization problems
Combining the modified Polak-Ribiere-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems
The linear conjugate gradient method was proposed by Hestenes and Stiefel [1] in the 1950s as an iterative method for solving linear systems
Summary
Due to their simplicity and their low memory requirement, the conjugate gradient methods play a very important role for solving unconstrained optimization problems, especially for the large-scale optimization problems. For general nonlinear function, an example given by Powell [8] shows that the PRP method may fail to be globally convergent even if the exact line search is used. Where F : Rn → Rn is continuously differentiable, and proposed a descent derivative-free method for solving symmetric nonlinear equations. The MPRP method reserves good properties of the PRP method and possesses another nice property; that it is, always generates descent directions for the objective function. This property is independent of the line search used. Combining the Zoutendijk feasible direction method with MPRP method, we propose a conjugate gradient type method for solving the nonnegative constraints optimization problems. The numerical results show that the method that we propose outperforms the Zoutendijk feasible direction method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
