A parametric solution algorithm for a class of rank-two nonconvex programs

The aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm lies within the class of the so called “optimal level solutions” parametric methods. The subproblems obtained by means of this parametrical approach are quadratic convex ones, but not necessarily neither strictly convex nor linear. For this very reason, in order to solve in an unifying framework all of the considered rank-two nonconvex programs a new approach needs to be proposed. The efficiency of the algorithm is improved by means of the use of underestimation functions. The results of a computational test are provided and discussed.