ENCE 724 / BMGT 832 Nonlinear Programming
Course Syllabus
Course Description
ENCE 724/BMGT 832 Nonlinear Programming Provide mathematically rigorous motivation and introduction to nonlinear programming theory, relevant to numerous problems in economics, engineering, and other disciplines. We will concentrate on models the necessary and sufficient conditions for optimality of nonlinear programs. Areas that will be covered include:
- Classification of optimization problems, definitions of local vs. global optimality, examples, directional differentiability
- Existence and uniqueness results for nonlinear programs
- Derivation of necessary and sufficient conditions for unconstrained nonlinear program
- Derivation of necessary and sufficient conditions for constrained nonlinear programs (not specific to Karush-Kuhn-Tucker conditions)
- Motivation and derivation of Karush-Kuhn-Tucker optimality conditions from both a geometric and algebraic perspective
- Duality theory for nonlinear program
- Second order optimality conditions for constrained problems
- Equilibrium problems as extensions to the KKT conditions: nonlinear complementarity and variational inequality formulation
- Algorithms to solve optimization and equilibrium problems
Textbook
Course textbook:
- M.S. Bazaraa, H.D. Sherali, C.M. Shetty, Nonlinear Programming Theory and Algorithms, John Wiley & Sons, Inc., 1979 (second or third editions, we'll be using the most up to date one though).
Other texts (not required) that may be of some help are:
- S. G. Nash and A. Sofer, Linear and Nonlinear Programming, The McGraw-Hill Companies, Inc., New York, 1996.
- A.J. Conejo, E. Castillo, R. Minguez, R. Garcia-Bertrand, Decomposition Techniques in Mathematical Programming Engineering and Science Applications, Springer, Berlin, 2006.
(see also web page for course for additional suggested references)
Course Objective
- Provide understanding for theory behind nonlinear programming problems and extensions to equilibrium problems
- Provide understanding of optimality conditions (KKT and otherwise) relevant to these problems
- Present algorithms to solve these problems.
Instructor
Dr. Steven A. Gabriel
Office EGR 1143
Telephone (301) 405-3242; Fax: (301) 405-2585
sgabriel@umd.edu
Grading
Grading is based on comprehension and mastery of the material.
- Homeworks (students hand in) 20%
- Max{in-class exam #1, in-class exam #2} 35%
- Min{in-class exam #1, in-class exam #2} 25%
- Final project (proposal, presentation, report) 20%
Course Policies
Students are encouraged to attend all lectures since the take-home exam and the homeworks will be closely related to material discussed in lectures. In addition, class participation is taken into account as part of the homework grade.
It is assumed that students will complete the homeworks by themselves although casual discussion with other class members is allowed. Homeworks will generally be given out each week and due at the start of class one week later.
The course is subject to the Code of Academic Integrity available on the web. The Code prohibits students from cheating on exams, plagiarizing papers, submitting the same paper for credit in two courses without authorization, buying papers, submitting fraudulent documents, and forging signatures.
The University has a legal obligation to provide appropriate accommodations for students with disabilities. Please inform Dr. Gabriel of any accommodations needed relative to disabilities. Also, University of Maryland policy states that students should not be penalized due to observances of their religious beliefs. Please inform Dr. Gabriel of such instances well in advance so that appropriate steps can be taken.
Short Bio on Dr. Gabriel
Academic Experience: Besides teaching at University of Maryland, Dr. Gabriel has held appointments in the Mathematical Sciences Department at The Johns Hopkins University, and in the Engineering Management and Systems Engineering Department at The George Washington University. In addition, he has served as a postdoctoral researcher in the Mathematics and Computer Science Division at Argonne National Laboratory.
Industry Experience: Dr. Gabriel has over 15 years of industry experience involving mathematical modeling of engineering-economic systems with applications in energy, transportation, service performance, and operations management. His specialties include optimization/equilibrium modeling, econometrics, decision support systems, and software development. His most recent industry experience includes 5 years as a Project Manager at ICF Consulting (www.icfconsulting.com) involving projects with their oil and gas group (www.icf-oilandgas.com) as well as their electrical power group.
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