A finite step-size procedure for the F-W method

摘要

The F-W Method for the NLP problem with linear constraints requires in its one-dimensional subproblem an exact solution, which cannot be obtained by a finite search procedure. Goldstein has used in unconstrained optimization a one-dimensional subproblem for which any point within certain real-line intervals is an acceptable solution. A similar subproblem can be applied to the F-W Method. A search procedure for such a subproblem is given and proven finite. A stopping rule for the algorithm is also given and proven ϵ-convergent to a K-T point, thus making the algorithm computationally implementable. Numerous applications to a complex banking problem have shown excellent results.