An Extended Frank-Wolfe Algorithm with Application to Portfolio Selection Problems

Abstract

This paper develops an extended Frank-Wolfe algorithm that utilizes approximate gradient and objective function evaluations at each iteration. A general convergence proof is given for the case when one wishes to maximize a concave function over a compact convex set. The algorithm is particularly useful for the solution of portfolio selection problems because: a) the special form of the constraint set renders the direction finding problem trivial, and b) exact gradient and objective function evaluations are not generally possible because these expressions are defined by integrals; however, increasing accuracy in their evaluation is possible. The algorithm has been implemented and used in the solution and analysis of a number of portfolio selection and revision problems. Details of the implementation and illustrative results are given.KeywordsStochastic ProgramPortfolio SelectionPortfolio Selection ProblemFeasible DirectionObjective Function EvaluationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.