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

Applied Mathematics(A Journal of Chinese Universities) 2021年第3期36卷 370-389页

作者： Anmol Gupta Sanjay Kumar Department of Electronics and Communication Engineering Thapar Institute of Engineering and TechnologyPatiala 147004India

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 ***,a generally non-linear optimization problem containing exponential functions becomes a linear problem in *** this as motivation,this paper lays mathematical foundation of well-known classical Gauss-Newton minimization(CGNM)algorithm in the framework of *** paper formulates the mathematical derivation of proposed method named as multiplicative Gauss-Newton minimization(MGNM)method along with its convergence *** proposed method is generalized for n number of variables,and all its theoretical concepts are authenticated by simulation *** case studies have been conducted incorporating multiplicatively-linear and non-linear exponential *** 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,***,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 ***,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

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