Smooth Nonlinear Optimization in Rn

Tamás Rapcsák

This book is the first uniform, differential geometric approach to smooth nonlinear optimization. This advance allows the author to improve the sufficiency part of the Lagrange multiplier rule introduced in 1788 and to solve Fenchel's problem of level sets (1953) in the smooth case. Furthermore, this permits the author to replace convexity by geodesic convexity and apply it in complementarity systems, to study the nonlinear coordinate representations of smooth optimization problems, to describe the structure by tensors, to introduce a general framework for variable metric methods containing many basic nonlinear optimization algorithms, and - last but not least - to generate a class of polynomial interior point algorithms for linear optimization by a subclass of Riemannian metrics. Audience: The book is addressed to graduate students and researchers. The elementary notions necessary...