The efficiency of optimization methods based on line searches

In nonlinear multidimensional optimization line search techniques aim to compute an optimum value for the step length to take along the search direction. The use of line search is related to the globalization of the algorithm. In this paper eight line search techniques are tested. Six of them are defined by a search step followed by a local approximation of the function. Davies, Swann and Campey search technique is implemented in four and Golden Section in two of them. Quadratic and cubic approximations are then introduced. Finally Armijo and Curry–Altman–Armijo criteria complete the set. Goldstein–Armijo condition is then used to guarantee a sufficient decrease of the function. Numerical results show that Armijo and Curry–Altman–Armijo criteria are more efficient in the sense that they need less iterations and functions calculations. Between approximation techniques, cubic based interpolation is the most efficient.