AN EFFICIENT HYBRID DERIVATIVE-FREE PROJECTION ALGORITHM FOR CONSTRAINT NONLINEAR EQUATIONS | Zendy

Kanikar Muangchoo | Zendy

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AN EFFICIENT HYBRID DERIVATIVE-FREE PROJECTION ALGORITHM FOR CONSTRAINT NONLINEAR EQUATIONS

Author(s) -

Kanikar Muangchoo

Publication year - 2021

Publication title -

malaysian journal of science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.131

H-Index - 12

ISSN - 1394-3065

DOI - 10.22452/mjs.vol40no3.6

Subject(s) - conjugate gradient method , nonlinear conjugate gradient method , mathematics , lipschitz continuity , monotonic function , convergence (economics) , gradient descent , projection (relational algebra) , nonlinear system , projection method , constraint (computer aided design) , derivative (finance) , gradient method , derivation of the conjugate gradient method , dykstra's projection algorithm , conjugate residual method , algorithm , mathematical optimization , mathematical analysis , computer science , geometry , artificial neural network , physics , quantum mechanics , machine learning , financial economics , economics , economic growth

In this paper, by combining the Solodov and Svaiter projection technique with the conjugate gradient method for unconstrained optimization proposed by Mohamed et al. (2020), we develop a derivative-free conjugate gradient method to solve nonlinear equations with convex constraints. The proposed method involves a spectral parameter which satisfies the sufficient descent condition. The global convergence is proved under the assumption that the underlying mapping is Lipschitz continuous and satisfies a weaker monotonicity condition. Numerical experiment shows that the proposed method is efficient.

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