Global optimization method for maximizing the sum of difference of convex functions ratios over nonconvex region
A global optimization algorithm is presented for maximizing the sum of difference of convex functions ratios problem over nonconvex feasible region. This algorithm is based on branch and bound framework. To obtain a difference of convex programming, the considered problem is first reformulated by introducing new variables as few as possible. By using subgradient and convex envelope, the fundamental problem of estimating lower bound in the branch and bound algorithm is transformed into a relaxed linear programming problem which can be solved efficiently. Furthermore, the size of the relaxed linear programming problem does not change during the algorithm search. Lastly, the convergence of the algorithm is analyzed and the numerical results are reported.
global optimization difference of convex functions branch and bound sum of ratios 90c26 90c32