Abstract
Based on the Dai-Laio and Powell symmetric methods, we developed a new three – term conjugate gradient method for solving large-scale unconstrained optimization problem. The suggested method satisfies both the descent condition and the conjugacy condition. For uniformly convex function, under standard assumption the global convergence of the algorithm is proved. Finally, some numerical results of the proposed method are given.
Highlights
Conjugate Gradient (CG) method comprise a class of unconstrained optimization algorithms characterized by low memory requirements and strong global convergence properties [3] which made them popular for engineers and mathematicians engaged in solving large-scale problems in the following form: min f (x ), x R n
For example Narushima, Yab and Ford [10] have proposed a wider class of three term conjugate gradient methods which always satisfy the sufficient descent condition
In a performance profile plot, the top curve corresponds to the method that solved the most problems in a( iter) or or CPU time that was within a given factor of the best(( iter) or or CPU time)
Summary
Conjugate Gradient (CG) method comprise a class of unconstrained optimization algorithms characterized by low memory requirements and strong global convergence properties [3] which made them popular for engineers and mathematicians engaged in solving large-scale problems in the following form: min f (x ), x R n (1). For example Narushima, Yab and Ford [10] have proposed a wider class of three term conjugate gradient methods (called 3TCG) which always satisfy the sufficient descent condition. Liu and Xu in [9] was generalized the Perry conjugate gradient algorithm (13), the search directions were formulated as follows d ps k 1. Where k is parameter, which is symmetric Perry three-terms conjugate gradient methods. The aim of this section is to develop a modified three-terms conjugate gradient method named ( AKTCG say ) by using Powell Symmetric (PS) method (15) and Dai and Liao (DL) CG method (3) and (12). 0 the search direction d AKTCG reduces to the well-known Hestenes and Stiefel HS , if g.
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