The Effects of Errors in the Estimation of the Gradient on the Frank-Wolfe Algorithm, with Implications for Interactive Programming

This paper presents an investigation of the effects of errors in the estimation of the gradient of the objective function on the Frank-Wolfe nonlinear programming algorithm. The investigation was motivated by a desire to reconcile the use of interactive programming approaches to the solution of the multiple-criteria problem with utility models that allow for intransitive statements of indifference and preference. Results are provided regarding the ultimate convergence of the algorithm, and its initial convergence rate.