Relaxation Methods In Nonlinear Optimization Problems

Widely used techniques of solving optimization problems are penalty and Lagrangernmethods. The methods indicate candidates for the so lution depending on properties ofrnobjective function and a feasible set .In some conditions numerical comparisons amongrnthe candidates is the only way to determine the solution.rnRelaxation method is an iterative method for approximating the solution ofrnoptimization problems numerically.rnThis seminar paper consist three chapters. The first chapter introduces the notion ofrnrelaxation process and explains the behavior 0 f convex and strongly convex f unctionsrnwith respect to relaxation sequences. The second chapter is mainly about estimation ofrnrelaxation process of convex and strongly convex functions. Chapter three comprisesrndifferent techniques of constructing relaxation sequences.rnFinally, I would like to thank Prof. Dr. R. Dellllllich, my advisor, for his willing tornprovide materials and for many valuable discussions and suggestions with regard tornvarious improvement of the paper.

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