Kursprogramm
Content:
The lecture deals with the minimization of smooth nonlinear functions subject to constraints. 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.
The solution of optimization problems without constraints is the subject of Part I of the lecture.
Part II of the lecture addresses optimization problems with constraints and is structured as follows:
• Topology and first-order approximations of the feasible set,
• Alternative theorems, optimality conditions for constrained problems,
• Solution methods for constrained problems (penalty methods, multiplier methods, barrier methods, interior-point methods, SQP methods, quadratic optimization).
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: January 9, 2026.
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.
