An efficient algorithm for globally solving generalized linear multiplicative programming

Generalized linear multiplicative programming problems are difficult problems known to be NPNP-hard, and they frequently arise in various areas such as engineering, economics, finance, etc. At present, most of the global optimization algorithms for this kind of problems are mainly developed based on those kinds of branch and bound algorithms. In this study, a new algorithm based on the concept of level set is presented for globally solving generalized linear multiplicative programming problems. The proposed algorithm is concise and easy to implement, so it is quite suitable for engineering applications. Finally, the global convergence is presented and the practical efficiency of the algorithm is demonstrated by the numerical experiments.