In each iteration k, the (dual) quasiNewton, conjugate gradient, and NewtonRaphson minimization techniques use iterative linesearch algorithms that try to optimize a linear, quadratic, or cubic approximation of f along a feasible descent search direction ,

by computing an approximately optimal scalar .
Therefore, a linesearch algorithm is an iterative process that optimizes a nonlinear function of one parameter () within each iteration k of the optimization technique. Since the outside iteration process is based only on the approximation of the objective function, the inside iteration of the linesearch algorithm does not have to be perfect. Usually, it is satisfactory that the choice of significantly reduces (in a minimization) the objective function. Criteria often used for termination of linesearch algorithms are the Goldstein conditions (see Fletcher 1987).
You can select various linesearch algorithms by specifying the LINESEARCH= option. The linesearch method LINESEARCH=2 seems to be superior when function evaluation consumes significantly less computation time than gradient evaluation. Therefore, LINESEARCH=2 is the default method for NewtonRaphson, (dual) quasiNewton, and conjugate gradient optimizations.
You can modify the linesearch methods LINESEARCH=2 and LINESEARCH=3 to be exact line searches by using the LSPRECISION= option and specifying the parameter described in Fletcher (1987). The linesearch methods LINESEARCH=1, LINESEARCH=2, and LINESEARCH=3 satisfy the leftside and rightside Goldstein conditions (see Fletcher 1987). When derivatives are available, the linesearch methods LINESEARCH=6, LINESEARCH=7, and LINESEARCH=8 try to satisfy the rightside Goldstein condition; if derivatives are not available, these linesearch algorithms use only function calls.