A nonquadratic one dimensional interpolation method for optimization

Abstract

The minimization of a function along a line is one of the most important problems in Optimization. A new algorithm, based on a rational function is examined and the order of convergence is considered. The rate of convergence is proved to be superlinear and the average rate of convergence of the rational model is compared to that of higher order polynomials. Numerical tests on a set of examples ascertain the reliability and efficiency of the algorithm.

Keywords:

• Optimization techniques
• rate of convergence
• nonquadratic model
• one dimensional interpolation