The convergence properties of some new conjugate gradient methods. (English) Zbl 1116.65073
A new conjugate gradient formula \(\beta^*_k\) is given to compute the search directions for unconstrained optimization problems. General convergence results for the proposed formula with exact Wolfe-Powell line search and Grippo-Lucidi line search. Under these line searches and some assumptions, the global convergence properties of the given methods are discussed. The given formula \(\beta^*_k\geq 0\) has the similar form as \(\beta^{PRP}_k\). Some numerical results show that the proposed methods are efficient.
Reviewer: Stefan Mititelu (Bucureşti)
MSC:
| 65K05 | Numerical mathematical programming methods |
| 90C59 | Approximation methods and heuristics in mathematical programming |
| 90C30 | Nonlinear programming |
Keywords:
nonlinear optimization; conjugate gradient; exact line search; inexact line search; global convergence; unconstrained optimization problem; numerical resultsReferences:
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