An SQP approach with line search for a system of nonlinear equations

Authors:
Pu-Yan Nie
Affiliations:
Department of Mathematics, Jinan University, Guangzhou, 510632, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2006

Citing 4
Cited 1

A recursive quadratic programming algorithm that uses differentiable exact penalty functions

Mathematical Programming: Series A and B
A trust region algorithm for equality constrained optimization

Mathematical Programming: Series A and B
Exclusion Regions for Systems of Equations

SIAM Journal on Numerical Analysis
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)

A line search filter approach for the system of nonlinear equations

Computers & Mathematics with Applications

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Abstract

In this paper, a line search sequential quadratic programming (SQP) approach to a system of nonlinear equations (SNE) is taken. In this method, the system of nonlinear equations is transformed into a constrained nonlinear programming problem at each step, which is then solved using SQP algorithms with a line search strategy. Furthermore, at each step, some equations, which are satisfied at the current point, are treated as constraints and the others act as objective functions. In essence, constrained optimization strategies are utilized to cope with the system of nonlinear equations.