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In this work, we propose a novel algorithm to perform spectral conjugate gradient descent for an unconstrained, nonlinear optimization problem. First, we theoretically prove that the proposed method satisfies the sufficient descent condition, the conjugacy condition, and the global convergence theorem. The experimental setup uses Powell’s conjugacy condition coupled with a cubic polynomial line search using strong Wolfe conditions to ensure quick convergence. The experimental results demonstrate that the proposed method shows superior performance in terms of the number of iterations to convergence and the number of function evaluations when compared to traditional methods such as Liu and Storey (LS) and Conjugate Descent (CD).

New spectral LS conjugate gradient method for nonlinear unconstrained optimization