A multiplicative Gauss-Newton minimization algorithm:Theory and application to exponential functions  

作　　者：Anmol Gupta Sanjay Kumar 

机构地区：[1]Department of Electronics and Communication Engineering,Thapar Institute of Engineering and Technology,Patiala 147004,India

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2021年第3期370-389,共20页高校应用数学学报（英文版）（B辑）

摘　　要：Multiplicative calculus(MUC)measures the rate of change of function in terms of ratios,which makes the exponential functions significantly linear in the framework of MUC.Therefore,a generally non-linear optimization problem containing exponential functions becomes a linear problem in MUC.Taking this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of MUC.This paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence properties.The proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation results.Two case studies have been conducted incorporating multiplicatively-linear and non-linear exponential functions.From simulation results,it has been observed that proposed MGNM method converges for 12972 points,out of 19600 points considered while optimizing multiplicatively-linear exponential function,whereas CGNM and multiplicative Newton minimization methods converge for only 2111 and 9922 points,respectively.Furthermore,for a given set of initial value,the proposed MGNM converges only after 2 iterations as compared to 5 iterations taken by other methods.A similar pattern is observed for multiplicatively-non-linear exponential function.Therefore,it can be said that proposed method converges faster and for large range of initial values as compared to conventional methods.

关 键 词：multiplicative calculus multiplicative least square method multiplicative Newton minimization multiplicative Gauss-Newton minimization non-linear exponential functions 

分 类 号：O172[理学—数学]