A branch and contract algorithm for problems with concave univariate, bilinear and linear fractional terms

A new deterministic branch and bound algorithm is presented in this paper f or the global optimization of continuous problems that involve concave univ ariate, bilinear and linear fractional terms. The proposed algorithm, the b ranch and contract algorithm, relies on the use of a bounds-contraction sub problem that aims at reducing the size of the search region by eliminating portions of the domain in which the objective function takes only values ab ove a known upper bound. The solution of contraction subproblems at selecte d branch and bound nodes is performed within a finite contraction operation that helps reducing the total number of nodes in the branch and bound solu tion tree. The use of the proposed algorithm is illustrated with several nu merical examples.