Relaxation Methods in Nonlinear Optimization Problems

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Addis Ababa University


Widely used techniques of solving optimization problems are penalty and Lagrange methods. The methods indicate candidates for the so lution depending on properties of objective function and a feasible set .In some conditions numerical comparisons among the candidates is the only way to determine the solution. Relaxation method is an iterative method for approximating the solution of optimization problems numerically. This seminar paper consist three chapters. The first chapter introduces the notion of relaxation process and explains the behavior 0 f convex and strongly convex f unctions with respect to relaxation sequences. The second chapter is mainly about estimation of relaxation process of convex and strongly convex functions. Chapter three comprises different techniques of constructing relaxation sequences. Finally, I would like to thank Prof. Dr. R. Dellllllich, my advisor, for his willing to provide materials and for many valuable discussions and suggestions with regard to various improvement of the paper.