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# Alternate Iterative Algorithms for Minimization of Non-linear Functions

 K. Karthikeyan Associate Professor, Mathematics division, VIT University, Vellore, Tamil nadu, India Related article at Pubmed, Scholar Google

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## Abstract

Numerical Optimization algorithms presents the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems. In this article, we propose some alternative iterative algorithms, with different order of convergence for minimization of non-linear functions. Then comparative study among the proposed algorithms and Newton’s algorithm is established by means of examples

### Keywords

Non-linear functions, Newton’s method, Ostrowski’s method, Eighth-order Convergence

### INTRODUCTION

Vinay Kanwar et al. [18] introduced new algorithms called, external touch technique and orthogonal intersection technique for solving the non linear equations. A.M.Ostrowski’s[5] introduced fourth order convergence iteration scheme for solving non linear equations. Sharma and Guha[7] introduced a family of modified Ostrowski’s methods with accelerated sixth order convergence. Chun and Ham [11] proposed some sixth order variants of Ostrowski’s root finding methods. Kou. et al [15] introduced some variants of Ostrowski’s method with seventh order convergence. Grau et.al[4] proposed an improvement to Ostrowski’s root finding method. Miquel Grau-Sanchez[19] proposed improvements of the efficiency of some three step iterative like Newton’s methods. Recently, Jisheng Kou and Xiuhua Wang [ 20] introduced some improvements of Ostrowski’s method with order of convergence eight. In this article, we introduce alternative algorithms for minimization of non linear functions and comparative study is established among the new seven algorithms with Newton’s algorithm by means of examples.

### CONCLUSION

In this paper, we introduced seven alternative numerical algorithms for minimization of nonlinear unconstrained optimization problems and compared with Newton’s method. It is clear from the above numerical results that the rate of convergence of algorithm (1) to algorithm(7) are in general faster than Newton’s algorithm. In particular algorithm(5) and algorithm (4) converge much better than the remaining algorithms. In real life problems, the variables can not be chosen arbitrarily rather they have to satisfy certain specified conditions called constraints. Such problems are known as constrained optimization problems. In near future, we have a plan to extend the proposed new algorithms to constrained optimization problems.

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