PERFORMANCE EVALUATION OF ITERATIVE METHODS TO UNCONSTRAINED SINGLE VARIABLE MINIMIZATION PROBLEMS

Linear programming problems can be solved with high precision using reliable and fast IPM (interior-point methods) algorithms. There are optimization tasks, however, that do not meet linearity requirement, dominating in real-life. If the decision variables are numbers of unknown values and objective function is nonlinear, the problem falls in the category of unconstrained nonlinear programming. The methods presented below concentrate on minimizing objective function which is not to stringent requirement, since all results can be obtained for maximization problem as well. Among general nonlinear programming problems one can identify dedicated and effective methods or special structures of the tasks. There is a variety of approaches to solving nonlinear programs, thus there is no method to solve the problems in general. As in the case of unconstrained minimization problems, one can divide the methods available to classes, such as zero-, firstand second-order algorithms. In some methods, necessary and sufficient optimality conditions are used, leading to obtaining the algorithms described in this paper. The paper concentrates on presenting three classes of algorithms with information concerning efficiency of the algorithms given, defined as mean number of iterations necessary to reach the minimizer with a prescribed tolerance. The conclusions can be helpful in selecting the algorithm dedicated to the problem to be solved.