دانلود کتاب بهینه سازی مبتنی بر جمعیت بر روی منیفولدهای ریمانی

Geometry has a significant role in the advancements of many fields of modern science, and most recently it has been brought under the limelight of information theory and artificial intelligence. Statistical models can be endowed with specialized geometrical structures, and data measurements can be viewed as points on an underlying manifold, a generalization of n-dimensional geometrical objects, rather than on Euclidean spaces. This chapter overviews the recent advancements in geometry and optimization theories, and outlines how both the manifold of data and the manifold of statistical models can be combined to construct optimization algorithms from geometrical principles. A detailed book synopsis is included in the chapter to guide the readers through the rest of the chapters.