The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Optimization Techniques on Affine Differential Manifolds


Ali S Rasheed, Faik Mayah and Ahmed A H AL-Jumaili

Ministry of Higher Education and Scientific Research,

Department of Physics, College of Sciences,
University of Wasit,


In addition to solid ground of Riemannian manifolds fundamentals, this article interviews some popular optimization methods on Riemannian manifolds. Several optimization problems can be better stated on manifolds rather than Euclidean space, such as interior point methods, which in turns based on self-concordant functions (logarithmic barrier functions). Optimization schemes like the steepest descent scheme, the Newton scheme, and others can be extended to Riemannian manifolds. This paper introduces some Riemannian and non-Riemannian schemes on manifolds.

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