A new modified HS algorithm with strong Powell-Wolfe line search for unconstrained optimization

Optimization is now considered a branch of computational science. This ethos seeks to answer the question «what best?» by looking at problems where quality any can be expressed numerically. One most well-known methods for solving nonlinear, unrestricted optimization conjugate gradient (CG) method. The Hestenes and Stiefel (HS-CG) formula one century’s oldest effective formulas. When using an exact line search, HS method achieves global convergence; however, this not guaranteed when inexact search (ILS). Furthermore, does always satisfy descent property. goal work create new (modified) reformulating classic parameter HS-CG adding term formula. It critical that proposed generates sufficient property (SDP) direction with Wolfe-Powell (sWPLS) every iteration, convergence (GCP) general non-convex functions guaranteed. Using sWPLS, modified (mHS-CG) has SDP regardless type guarantees GCP. advantage keeping scalar non-negative sWPLS. paper significant in it quantifies how much better modification performance compared standard methods. As result, numerical experiments between mHSCG sWPL problem show CG more robust than without