Optimality Conditions And The Method Of Convexification And Concavification For Global Optimization

Several new optimality conditions for global optimization problem are proposed in this paper which contains four chapters. Global optimization problems' history and the development are introduced in the first chapter. And then some fundamental definitions and conclusions are proposed in the second chapter. In the third chapter several new optimality conditions are studied : H-differential method. First H-differential and H-norma1 form are presented according to the L-subdifferential and then the H-differential set is also presented according to the H-differential. H-differential is a set of functions which are nonlinear functions. After that some necessary and sufficient conditions of global optimization have been obtained in terms of H-differential and H-norma1 form of special functions. In the last chapter a new method of convexification and concavification is also proposed by the definition of the subdefinite functions for the nonlinear programming problem in which the objective function is non-convex, non-concave, non-monotonous. With the objective function's direct convexification or concavification, the global optimal solution can be easily reached.