Study On Deterministic Algorithms For Global Optimization Problem

Global optimization addresses the computation and characterization of global solutions to nonlinear function.The main task of global optimization is to determine(with theoretical guarantees) an approximate global optimal solution of the objective function with a set of constraints or unconstraint.Due to the development of science and technology,the global optimization problems are often discovered in the field of economic planning administration,engineering design, production management,traffic transportation,national defence and so on.It has attracted extensive attention.Two methods on global optimization have been extended and improved in this paper.This paper consists of four chapters.In the first chapter,several basis concepts and characters on generally nonlinear programming are introduced.Then some typical methods for global optimization problems are briefly presented.The next three chapters are main contents of this paper.In the second chapter,a novel cut-peak function method for global optimization problems is mainly introduced.Then a new and different cut-peak function who has better analytical character is used to solve box-constrained global minimization problems.Some numerical tests demonstrate the more efficiency of the new cut-peak function algorithm.In the third chapter,the cut-peak function method for box-constrained global optimization is extended to linearly constrained global optimization.By controlling the step-size,iterative sequences have been restricted in the feasible area when the algorithm executes.Then the results of the numerical tests demonstrate the validity of the algorithm.In the fourth chapter,the impelling function method for unconstrained global optimization problems is discussed.Then a impelling function algorithm has been used to solve the linearly constrained global optimization problems.And some numerical results has been given in the last part.