# Nonlinear Optimization (6 ECTS)

Lecturer:   Dr. Andreas Sommer   ( ansommermail.uni-mannheim.de )
Lecture:  Tuesdays, 8:30 – 10:00 in Seminar Room II in B6 D 007
Exercise: Mondays, 8:30 – 10:00 in Seminar Room II in B6 D 007
The lecture is held in English.
Begin: 14.02.2023

Examination takes place in B6, Room 301

Materials

Introduction slides with formalia

Exercise Sheet #1  (Programming Solution: Ex1_sol.zip)
Exercise Sheet #2  (Programming Solution: Ex2_sol.zip) – Addendum
Exercise Sheet #3  (Note the due date)
Exercise Sheet #4  (Programming Solution: Ex4_sol.zip)
--- Performance comparison: timeGrowingArrays.m
Exercise Sheet #5  (Programming Solution: Ex5_sol.zip)
Exercise Sheet #6  (Programming Solution: Ex6_sol.zip)
Easter Challenge Sheet and data file LVdata.mat or LVdata.zip
Exercise Sheet #7  (Programming Solution: Ex7_sol.zip)
Exercise Sheet #8  (Programming Solution: Ex8_sol.zip)
Exercise Sheet #9
Exercise Sheet #10 (Programming Solution: Ex10_sol.zip)
Exercise Sheet #11

Lecture Script (updated 2023-04-29)

Course contents

The first part of the lecture copes with unconstrained nonlinear optimization problems. We formulate optimality conditions and discuss solution methods, with a focus on local descent methods like gradient- and Newton(like) methods, and their globalization using line-search methods.
The second part introduces solution theory and basic algorithms for constrainted optimization problems, especially penalty and SQP (sequential quadratic programming) methods.
The accompanying exercises will strengthen on the one hand the theoretical grounds, and on the other hand give practice on the application of introduced algorithms and methods, with a focus on efficient programming.
Matlab will be used during the course, however, the language for the programming exercises can be freely chosen.

Prerequisites

Knowledge corresponding to the modules Analysis I/II and Linear Algebra I/II, and ideally also Linear Optimisation. Basic skills in the use of MATLAB may be helpful.

Matlab (https://www.uni-mannheim.de/it/studierende/software/#c131177) licenses are available for all students of the University of Mannheim free of charge.
Alternatively, the partially compatible open source alternative GNU Octave (https://octave.org/) can be used.

Literature:

• J. Nocedal and S. J. Wright, Numerical Optimization, Springer, Berlin, 2006.
• F. Jarre, J. Stoer: Optimierung, Springer Verlag.
• M. Ulbrich, S. Ulbrich, Nichtlineare Optimierung, Birkhäuser, 2012.
• D. Bertsekas, Nonlinear Programming, Athena Scientific Publisher, Belmont, Massachusetts, 1995.
•  A. R. Conn, N. I. M. Gould, P. L. Toint, Trust-Region Methods, SIAM, Philadelphia, 2000.
• J. E. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM Philadelphia, 1996.
• R. Fletcher, Practical Methods of Optimization, Wiley \& Sons Publisher, New York, 1980.
• C. T. Kelley, Iterative Methods for Optimization, Frontiers in Applied Mathematics, SIAM, Philadelphia, 1999.
• C. Geiger, C. Kanzow, Numerische Verfahren zur Lösung unrestringierter Optimierungsaufgaben, Springer-Verlag, Berlin, 1999.