Abstract
This article considers modified formulas for the standard conjugate gradient (CG) technique that is planned by Li and Fukushima. A new scalar parameter θkNew for this CG technique of unconstrained optimization is planned. The descent condition and global convergent property are established below using strong Wolfe conditions. Our numerical experiments show that the new proposed algorithms are more stable and economic as compared to some well-known standard CG methods.
Highlights
Conjugate gradient (CG) strategies consists of a category of nonlinear optimization algorithms, which needs low memory and powerful local and global convergence properties [1,2]
On the understanding that the function is defined in the form f: Rn ⟶ R is smooth nonlinear function. e repetitive formula is in the form xk+1 xk + αkdk
A New Scalar Formula for the Parameter θNk ew. In this part of this article, we proposed a new version for the parameter θk by relying on the modified BFGS Journal of Mathematics method proposed by Li and Fukushima [1]
Summary
Conjugate gradient (CG) strategies consists of a category of nonlinear optimization algorithms, which needs low memory and powerful local and global convergence properties [1,2]. E most important component of this formula is αk step-size, and the search direction dk consists of dk+1. E step-size αk is sometimes chosen to satisfy bound line search condition [3]. Among these search direction conditions, the strong Wolfe line search condition is sometimes outlined as follows:. Ere are many different formulas for conjugate coefficients as in the following sources, e.g., Hestenes and Stiefel, HS [4]; Fletcher and Reeves, FR [5]; Polak and Ribiere, PR [6]; Conjugate Descent, CD [7]; Li and Fukushima, LF [1]; and Liu and Story, LS [8], correspond to different choice for the scalar parameter βk 0 < δ < σ < 1. ere are many different formulas for conjugate coefficients as in the following sources, e.g., Hestenes and Stiefel, HS [4]; Fletcher and Reeves, FR [5]; Polak and Ribiere, PR [6]; Conjugate Descent, CD [7]; Li and Fukushima, LF [1]; and Liu and Story, LS [8], correspond to different choice for the scalar parameter βk
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