A Monotonic Optimization Approach For Two Types Of Programming Problems

Global optimization has been widely used in the fields of molecular biology, economic, environmental engineering, information technology, industrial manufacturing and so on. Especially for generalized quadratic programming and generalized geometric programming problem can be applied to investment combination. This paper respectively proposes monotonic optimization algorithms for solving generalized quadratic programming problem and generalized geometric programming problem. The main contents of this paper are as follows:In Chapter1, The latest research development of problems studied in this paper are simply presented, and a brief introduction is given to related concepts of complexity and our work.In Chapter2, A monotonic optimization approach for generalized quadratic program-ming. In the algorithm, the original problem is first converted into an equivalent monotonic optimization problem whose objective function is just a simple univariate by exploiting the particularity of this problem. Then, a range division and compression approach is used to reduce the range of each variable. Tightening variable bounds iteratively allows the proposed method to reach an approximate solution within an acceptable error by using monotonic functions, in which such solution is adequately guaranteed to be feasible and to be close to the actual global optimal solution. The numerical examples and random experiment snow that the algorithm is feasible. In Chapter3, the new global optimization algorithm which is mentioned in chapter2is applied to the generalized geometric programming problem. According to the features of the generalized geometric programming problem, it can be transformed into an monotonic optimization problem. Furthermore, we analyse the key steps about the branch and bound, cut. Compared with other methods, numerical results vindicate that the new algorithm is feasible.