A systematic search method for obtaining multiple local optimal solutions of nonlinear programming problems

The authors propose a systematic method to find several local minima for general nonlinear optimizatioin problems. They develop some analytical results for a quasi-gradient system and reflected gradient system and apply them to explore the topological aspects of the critical points of the objective function. By properly switching between a quasi-gradient system and a reflected gradient system, the proposed method can obtain a set of local minima.<<ETX>>

[1]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[2]  Aimo A. Törn,et al.  Global Optimization , 1999, Science.

[3]  M. Hirsch,et al.  Differential Equations, Dynamical Systems, and Linear Algebra , 1974 .

[4]  Lazhar Fekih-Ahmed.  New theoretical results on stability regions and bifurcations of nonlinear dynamical systems and their applications to electric power systems analysis , 1991 .

[5]  S. Smale.  On Gradient Dynamical Systems , 1961 .

[6]  Leon O. Chua,et al.  The identification of general pseudoreciprocal vector fields , 1992 .

[7]  Leon O. Chua,et al.  Global optimization: a naive approach , 1990 .

[8]  Felix F. Wu,et al.  Stability regions of nonlinear autonomous dynamical systems , 1988 .

[9]  Thomas F. Coleman,et al.  Large-Scale Numerical Optimization: Introduction and Overview , 1991 .

[10]  H. Th. Jongen,et al.  The index-k-stabilizing differential equation , 1981 .

[11]  C. DeMarco.  Approximating power system dynamics and energy functions by quasi-gradient models , 1989, IEEE International Symposium on Circuits and Systems,.

[12]  N. K. Sancheti,et al.  A new approach to global optimization using ideas from nonlinear stability theory , 1992, [Proceedings] 1992 IEEE International Symposium on Circuits and Systems.

[13]  J. Zaborszky,et al.  On the phase portrait of a class of large nonlinear dynamic systems such as the power system , 1988 .

[14]  Panos M. Pardalos,et al.  Constrained Global Optimization: Algorithms and Applications , 1987, Lecture Notes in Computer Science.

[15]  Hsiao-Dong Chiang,et al.  The closest unstable equilibrium point method for power system dynamic security assessment , 1989 .

[16]  S. Vavasis.  Nonlinear optimization: complexity issues , 1991 .

[17]  Felix F. Wu,et al.  Foundations of the potential energy boundary surface method for power system transient stability analysis , 1988 .

[18]  F. H. Branin.  Widely convergent method for finding multiple solutions of simultaneous nonlinear equations , 1972 .

[19]  Leon O. Chua,et al.  Practical Numerical Algorithms for Chaotic Systems , 1989 .