Effective algorithm for solving the generalized linear multiplicative problem with generalized polynomial constraints

In this study, we propose a novel global optimization algorithm for effectively solving the generalized linear multiplicative problem with generalized polynomial constraints. Based on the branch and bound scheme, the algorithm is implemented by solving its equivalent generalized geometric programming problem. In the algorithm, lower bounds are obtained by solving a sequence of linear lower bound relaxation problems, which can be derived using a new linearization technique. Finally, we prove the global convergence of the algorithm and some numerical results are presented that demonstrate the computational advantages of the proposed algorithm.