Algorithmische und Diskrete Mathematik | Fakultät für Mathematik

Nonlinear Optimization (M12)

Winter Term 2017/18

Content:	We discuss basic algorithmic approaches for solving smooth nonlinear optimization problems. Aspects of interest are convergence rate, computational efficiency and numerical behavior. Unconstrained Optimization: Newton and quasi-Newton methods, line search, trust regions, conjugate gradients, approximate and automatic differentation Constrained Optimization: Lagrange multipliers, quadratic programming, penalty, barrier and augmented Lagrangian methods, sequential quadratic programming.
Audience:	any Mathematics program starting from the 7th term (5th should be ok, too)
Requirements:	Linear Algebra, Analysis, Basics of Optimization

J. Nocedal, S.J. Wright; Numerical Optimization, Springer 1999;
Florian Jarre, Josef Stoer; Optimierung, Springer, 2nd ed., 2006. eBook ISBN 3-540-35447-5.
Carl Geiger, Christian Kanzow; Theorie und Numerik restringierter Optimierungsaufgaben, Springer, 2002. ISBN 3-540-42790-2.
J.F. Bonanns, J. C. Gilbert, C. A. Sagastizábal; Numerical Optimization; Springer 2003. ISBN 3-540-00191-3.
Bazaraa, Sherali, Shetty; Nonlinear Programming: Theory and Algorithms, Wiley, 1993
Luenberger; Linear and Nonlinear Programming, Addison-Wesley, 1984