Smooth Nonlinear Optimization in Rn

This is a differential geometric approach to smooth nonlinear optimization. This 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.