Some New Auxiliary Function Methods For Global Optimization

Global optimization is a very broad range of disciplines applied in real life, a lot ofproblems in the natural and social sciences can be attributed to a global optimizationproblem, global optimization is widely used in financial, economic models, networktraffic, image processing, molecular biology, chemical engineering design and control,environmental engineering, etc. When there are multiple local minima is different fromthe global minimum point in the global optimization problem, the classic solve linearprogramming problems technology can not be successfully applied to nonlinear globaloptimization problems. Moreover, the lack of a good criterion to determine a localminima is the global minimum point for a long time nonlinear global optimizationproblem has become optimization of a problem in the field of global optimization hasbecome the hot topic of research by scholars in recent years, after decades of researchand development, global optimization theory and methods has been greatly, and such astwo-stage method, random search methods, modern heuristic algorithm, intervalmethods, branch and bound method, the filled function method, the paper studiesstationary point function method (a new type ofauxiliary function method) and otheralgorithms.The basic idea of the stationary point function method: First, the existing localminimization algorithm (such as the conjugate gradient method, quasi-Newton method,etc.) to find a local minimum of the objective function, then this local minimumDepartment to construct an auxiliary function is a smooth point function, theminimization of the constructed stationary point function to find a better local minimumpoint of the original optimization problem, and then in the original optimizationproblem, a better local minimum point and then construct a new stationary pointfunction, continue on the new stationary point function to find the original optimizationproblem better local minima problem by implementing a series of local minima to theglobal minimum of this solution process by the local minima two-stage cycle of thecomponents: the first phase of the implementation of the original objective functionlocal minima; the second phase of implementation of the local minima on this newstationary point function or intended to be a stationary point function, while allowingthe original objective function is also a decline in the last local minimum can be used asthe original optimization problem approximate global minimum point.This paper is organized as follows: The first chapter is devoted to global optimization of the development status of the problem and already several specificalgorithms. Unconstrained global optimization problem with a new smooth function anda new quasi-stationary point function, and then were given a smooth function methodand the algorithm proposed stationary point function method, as well as their numericalresults. Chapter III of constrained global optimization problem, a new stationary pointfunction method and gives some numerical example. fourth draw total the conclusionsof this paper.