Nonmonotone spectral gradient method based on memoryless symmetric rank-one update for large-scale unconstrained optimization

<p style='text-indent:20px;'>This paper proposes a nonmonotone spectral gradient method for solving large-scale unconstrained optimization problems. The parameter is derived from the eigenvalues of an optimally sized memoryless symmetric rank-one matrix obtained under measure defined as ratio determinant updating over its largest eigenvalue. Coupled with line search strategy where backtracking-type applied selectively, acts stepsize during iterations when no performed and milder form quasi-Newton update backtracking employed. Convergence properties proposed are established uniformly convex functions. Extensive numerical experiments conducted results indicate that our outperforms some standard conjugate-gradient methods.</p>