Research On The Global Optimization Of Two Types Of Non-convex Programming Problems

This thesis mainly studies the global optimization algorithm of solving linear fractional programming problem and a kind of non-convex factorable programming problem. The thesis is divided into two parts, the main contents are stated as followsIn Chapter1, to a kind of linear fractional programming problems, a new branch and bound method is proposed. In this algorithm, the main features is that by utilizing the monotonicity and concave and convex sex of logarithmic function and exponential function and linear relaxation technique, a relaxation linear programming problem of equivalent problem of original problem is established, and a new second-relaxation linear programming is put forward to determine the lower bound of the optimal value of the original problem. This can be used to improve the convergence rate of the algorithm. Through the successive refinement of the linear relaxation of the feasible region and the solutions of a series of relaxation linear programming problems, and from theory the proof which the proposed branch and bound algorithm is convergent to the global minimum is given. And finally the numerical experiments are reported to shown the.feasibility of the proposed algorithm.In Chapter2, to a kind of non-convex factorable programming problems, a new seeond-relaxation linear programming is put forward to determine the low bound of optimal value, and a new branch procedure in which the upper bound of the optimal value is being adjusted better by obtained feasible points. So branch and bound method is combined with outer approximation method organizationally, and a global optimization algorithm is structured, and its convergence is proved.