Abstract

It is well known that several techniques in optimization require the construction of an initial polyhedral convex set whose vertices and extreme directions are easy to calculate. This short note is devoted to the construction of a well initiated polyhedron meaning that this set contains an optimal solution and is not beyond the domain where the objective function and constraints are defined. For optimization problems over the efficient set of a multiple objective linear program and bilevel linear programs the author makes use of outer and inner approximations for the construction of such a set. In case such a set is neither a simplex, a cone, nor a rectangle, then the author makes use of polyhedral bisection developed in convex-concave programming to obtain a decomposition branch-and-bound algorithm for solving bilevel linear programs.