Kursprogramm
Content:
The lecture covers the minimization of smooth nonlinear functions. For such problems, which occur very frequently in economics, engineering, and the natural sciences, we derive optimality conditions and present numerical solution methods based on them.
Part I of the lecture addresses optimization problems without constraints and is structured as follows:
• Introductory examples and terminology,
• Existence of optimal points,
• First- and second-order optimality conditions,
• Solution methods for unconstrained optimization problems (step size control, gradient methods, variable metric methods, Newton’s method, quasi-Newton methods, CG methods, trust-region methods).
The treatment of optimization problems with constraints is the subject of Part II of the lecture.
Additional Information:
Parts I and II of the lecture will be given consecutively within the same semester!
In the accompanying exercise session, you will have the opportunity, among other things, to implement some methods and test them on practice-oriented examples.
Exercises (Instructor: Stefan Schwarze)
Friday, 14:00 - 15:30, 10.91 - Oberer Hörsaal.
Start: October 31, 2025.
Literature:
W. ALT, Nichtlineare Optimierung, Vieweg, 2002.
M.S. BAZARAA, H.D. SHERALI, C.M. SHETTY, Nonlinear Programming, Wiley, 1993.
O. GÜLER, Foundations of Optimization, Springer, 2010.
H.Th. JONGEN, K. MEER, E. TRIESCH, Optimization Theory, Kluwer, 2004.
J. NOCEDAL, S. WRIGHT, Numerical Optimization, Springer, 2006.
O. STEIN, Basic Concepts of Nonlinear Optimization, Springer, 2024.
