Abstract
A new spectral conjugate gradient method (SDYCG) is presented for solving unconstrained optimization problems in this paper. Our method provides a new expression of spectral parameter. This formula ensures that the sufficient descent condition holds. The search direction in the SDYCG can be viewed as a combination of the spectral gradient and the Dai-Yuan conjugate gradient. The global convergence of the SDYCG is also obtained. Numerical results show that the SDYCG may be capable of solving large-scale nonlinear unconstrained optimization problems.
Highlights
As well known, a great deal of issues, which are studied in scientific research fields, can be translated to unconstrained optimization problems
In order to test the numerical performance of the SDYCG algorithm, we choose some unconstrained problems with the initial points from CUTEr library [12, 13]
We would like to compare the SDYCG with the CGDESCENT
Summary
A great deal of issues, which are studied in scientific research fields, can be translated to unconstrained optimization problems. Raydan introduced the spectral gradient method for large-scale unconstrained optimization in [7] He combined a nonmonotone line search strategy that guarantees global convergence with the Barzilai and Borwein method. Du and Chen [9] gave a modified spectral FR conjugate gradient method with Wolfe-type line search based on FR formula Their spectral parameters θk and βk are expressed as θk+1. Yu et al [10] presented a modification of spectral Perry’s conjugate gradient formula, which possessed the sufficient descent property independent of line search condition. Their search direction dk+1 is defined by (8) and βk has the form βkDSP βkSP. We draw some conclusions about our new spectral conjugate gradient method
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