Using nonlinear functions to approximate a new quasi-Newton method for unconstrained optimization problems.

Autor:	Dehghani, R., Bidabadi, N., Hosseini, M. M.
Předmět:	NONLINEAR functions QUASI-Newton methods HESSIAN matrices MATRIX functions EQUATIONS
Zdroj:	Numerical Algorithms; Jun2021, Vol. 87 Issue 2, p755-777, 23p
Abstrakt:	In order to get a higher order accuracy of approximating the Hessian matrix of the objective function, we use the chain rule and propose two modified secant equations. An interesting property of the proposed methods is that these utilize information from two most recent steps where the usual secant equation uses only the latest step information. The other point of interest to one of the proposed methods is that it makes use of both gradient and function value information. We show that the modified BFGS methods based on the new secant equations are globally convergent. The presented experimental results illustrate that the proposed methods are efficient. [ABSTRACT FROM AUTHOR]
Databáze:	Complementary Index
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