An efficient line search for nonlinear least squares

The line search subproblem in unconstrained optimization is concerned with finding an acceptable steplength which satisfies certain standard conditions. Prototype algorithms are described which guarantee finding such a step in a finite number of operations. This is achieved by first bracketing an interval of acceptable values and then reducing this bracket uniformly by the repeated use of sectioning in a systematic way. Some new theorems about convergence and termination of the line search are presented. Use of these algorithms to solve the line search subproblem in methods for nonlinear least squares is considered.