We propose a systematic method to find several local optimalsolutions for a general nonlinear optimization problem. Analyticalresults for quasi-gradient systems and reflected gradient systems aredeveloped and applied to explore the topological and geometric aspectsof the critical points of the objective function. A mechanism is devisedto escape from a local optimal solution and proceed into another localoptimal solution by locating the decomposition point. By properlyswitching between quasi-gradient systems and reflected gradient systems,our proposed method can obtain a set of local optimal solutions anddecomposition points. This algorithm also can find the global optimalsolution. It depends on its ability to find all the decompositionpoints. The main algorithm contains two levels: the lower level iscontinuous while the upper level is discrete in nature. Furtherimprovements in the algorithm to locate all decomposition points aredesirable. The proposed method is applied to one test example withencouraging results
展开▼
