A Multidimensional Bisection Method for Minimizing Function over Simplex

Abstract

Abstract—A new method for minimization problem over simplex, as a generalization of a well-known in onedimensional optimization bisection method is proposed. The convergence of the method for class of strictly unimodal functions including class of strictly convex functions is proved. The computational results are presented for a set of test problems. Index Terms — convex set, n-dimensional simplex, strictly unimodal function, direct search methods, nonlinear programming, nonlinear optimization. I.