Two Kinds Of Nonlinear Programming Problems Of Global Optimization

This thesis mainly studies two type of optimization problems based on the branch and bound algo-rithm:fractional programming and mixed integer programming problems. The thesis is divided into thr-ee parts. The main contents are arranged as follows:In Chapter 1, a new branch and bound algorithm is proposed for sum of linear fractional program-ming problem with coefficient. In this algorithm, firstly, obtains the equivalent non-convex optimization model of the original problem. Secondly, establishes the linear relaxation programming problem of ori-ginal problem by utilizing the linearlizing technique. Through the successive refinement of the feasible region and the solution of a series of the relaxation linear programming problem, the upper and lower bounds of global optimal value are continuously updated, and from theory the proof which the proposed branch and bound algorithm is convergent to the global minimum is given. Finally, the numerical experiments are reported to show the feasibility of the proposed algorithm.In Chapter 2, a new branch and bound algorithm is studied for a kind of concave-convex fractional programming problem. In this algorithm, firstly, we transform the original problem into the concave minimization problem that the numerator is concave function and the denominator is linear function. T-hen, to the equal problem, we proposed branch and bound algorithm based on the value interval of denominators. The linear programming relaxation technique is used to determine the lower bound of the optimal value of the original problem. The numerical experiments are reported to show the feasibility of the proposed algorithm.In Chapter 3, a new global optimization algorithm for locating global minimum of a signomial mi-xed integer nonlinear programming problems with free variables. In this algorithm, free variables in ori-ginal problem are first transformed into positive variables by utilizing equivalent transformation, then utilize a new convexication relaxation lower-bounding strategies, make the non-convex programming problem can be converted to a sequence of convex programming problem, in order to obtain the lower bound of the optimal value of the original problem, and proved the convergence of the proposed branch and bound algorithm.