Titlebook: Introduction to the Theory of Nonlinear Optimization; Johannes Jahn Textbook 2020Latest edition The Editor(s) (if applicable) and The Auth

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Textbook 2020Latest editionons together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, extended semidefinite optimization, and an investigation of linear quadratic and time minimal control problems. The 4.th. edition of this book has been extensively revised

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Textbook 2020Latest editionand a new chapter on discrete-continuous optimization has been added. This textbook focuses on the fundamentals, with particular emphasis on their application to problems in the calculus of variations, approximation and optimal control theory. The reader is assumed to have a basic grasp of linear functional analysis..

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Generalized Lagrange Multiplier Rule,condition. The optimality condition presented generalizes the known multiplier rule published by Lagrange in 1797. With the aid of this optimality condition we deduce then the Pontryagin maximum principle known from control theory.

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Extension to Discrete-Continuous Problems,. is only limitedly applicable. For a Lagrange theory and a duality theory in discrete-continuous nonlinear optimization one needs a different approach, which is developed in this chapter. The main key for such a theory is a special separation theorem for discrete sets. Using this theory we present optimality conditions as well as duality results.

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