A new descent algorithm with curve search rule

In the paper we present a new descent algorithm with curve search rule for unconstrained minimization problems. At each iteration, the next iterative point is determined by means of a curve search rule. It is particular that the search direction and the step-size is determined simultaneously at each iteration of the new algorithm. The algorithm, similarly to conjugate gradient methods, avoids the computation and storage of some matrices associated with the Hessian of objective functions. Unlike ODE methods, it is not required to solve ordinary differential equations at each iteration. Although the convergence rate of our algorithm is not as fast as that of Newton-like methods, it is suitable to solve large scale minimization problems.