Symmetric Perry conjugate gradient method

Abstract

A family of new conjugate gradient methods is proposed based on Perry's idea, which satisfies the descent property or the sufficient descent property for any line search. In addition, based on the scaling technology and the restarting strategy, a family of scaling symmetric Perry conjugate gradient methods with restarting procedures is presented. The memoryless BFGS method and the SCALCG method are the special forms of the two families of new methods, respectively. Moreover, several concrete new algorithms are suggested. Under Wolfe line searches, the global convergence of the two families of the new methods is proven by the spectral analysis for uniformly convex functions and nonconvex functions. The preliminary numerical comparisons with CG_DESCENT and SCALCG algorithms show that these new algorithms are very effective algorithms for the large-scale unconstrained optimization problems. Finally, a remark for further research is suggested.

A new optimization method based on Perry's idea through the use of the matrix power

“…In this section, we discuss the efficiency of our new version of GPP algorithm by comparing it with the CG-DESCENT algorithm of Hager and Zhang [22], the mBFGS algorithm [23] and the SPDOC algorithm [24]. To determine the performance of all algorithms on a set of unconstrained optimization test problems [25], each problem is tested for a number of variables: 2, 10, 50, 100, 1000, 1500, 2000, 5000, and 10000 so that the total number of test problems is the 80 unconstrained problems.…”

Three-terms conjugate gradient algorithm based on the Dai-Liao and the Powell symmetric methods

“…Furthermore, Liu and Xu in [9] was generalized the Perry conjugate gradient algorithm (13), the search directions were formulated as follows…”

A modified three-term conjugate gradient method for large –scale optimization

“…Let 𝑑 𝑘+1 Search direction and 𝑘 ≥ 0 it is born with formula (1.27) it is that size of the line and the verification of the condition and the thousand Wolfe then 𝑑 𝑘+1 Check your own beef (1.28). Proof: To proof by pattern in the sports induction 1-when 𝑘 = 0 the 𝑑 1 = −𝑔 1 → 𝑑 By the following property we gat [16]. 𝑢 𝑇 𝑣 ≤ By the following property we gat…”