A New Conjugate Gradient Formula And Its Applications

Due to its simplicity and its very tow memory requirement, the conjugate gradient(CG) method has played a special role for solving large-scale unconstrained nonlinear op-timization problelns. In already-existing conjugate gradient methods, FR method has niceglobal convergent properties, but its numerical performance is inferior to PRP method;some methods, such as PRP and HS Inethods, which have nice numerical performance, arenot global convergent under some mild conditions. In this paper, a new conjugate gradi-ent formulaβ_k~* is given to compute the search directions for unconstrained optimizationproblems.We get the the following main results in this thesis: (1) the search directions d_kwhich are generated by the givenβ_k~* under the strong Wolfe-Powell line search satisfy thesufficient descent condition; (2) the conjugate gradient method with the givenβ_k~* under thestrong Wolfe-Powell line search is convergent globally; (3) the same strategy can be usedto HS and LS methods to deduce others new parameters which have the similar convergentproperties withβ_k~* (4) all the proposed methods have nice numerical performance.