Finding ways of recognizing global optimum is the very fundamental, unsolved problem in existing optimization theories. We can not establish a true theory of optimization without it. Also, it is very hard to construct effective algorithms for finding global optimum. This paper presented a new optimization principle, called cooperative optimization, for solving this extremely important problem in optimization theory. A number of global optimality conditions are provided in a general form. The application of cooperative optimization in coding yields near-perfect results in finding global optima, significantly better than the most powerful optimization algorithm ever found so far.