Course description:

Formulation and solution of continuous optimization problems in engineering design. This course will cover optimization of engineering systems, emphasizing how to formulate problems so that you can apply off-the-shelf software to solve them. We will use  MATLAB in the course, motivating the analysis and algorithms with a number of case studies. The main areas of study will be: solution of simultaneous equations and non-linear optimization problems.

The course illustrates how to think about and describe problems to make them amenable to solution by optimization software.  In brief: formulation of problems to facilitate their solution.  Five general problem classes are considered:

• linear systems of equations,

• non-linear systems of equations,

• unconstrained optimization,

• equality-constrained optimization, and

• inequality-constrained optimization.

Topics to be covered in the class will include: characteristics of problems and their solutions, transformation of problems, formulation of linear simultaneous equations problems, solution of linear simultaneous equations, sparsity of linear equations and sparsity techniques, sensitivity analysis for linear equations, formulation of non-linear simultaneous equations problems, solution of simultaneous equations by Newton's method, sensitivity analysis for non-linear equations, formulation of non-linear optimization problems, optimality conditions for convex non-linear programs, review of  "classical" optimization techniques, interior point techniques applied to convex non-linear problems, sensitivity analysis for optimization problems.

Expectations

I expect that you will spend seven to ten hours per week  outside of class on this course to read the lecture notes, review the class material, and work on homeworks.  I assume that you have a strong background and, moreover, there is a heavy homework burden in this class.  If you do not have the background for the class or you are not prepared to work diligently on long and hard homeworks, please do not sign up for this class!

I expect you to have read over lecture notes  ahead of class so that class time is used efficiently to explain concepts.  Lecture notes are posted at the instructor home page www.ece.utexas.edu/~baldick.  Look under "Teaching Plans and Course Web pages" for "Optimization of Engineering Systems."  There is also a downloadable file of Appendices that includes pre-requisite material together with an Errata to the textbook and to the homework exercises.

Please come to office hours with prepared questions.

I may have to cancel one or two classes during the semester in order to attend conferences.  We will schedule make-up classes for these cancelled classes since the semester will be extremely full of material to cover.

I do not take attendance and you are free to attend or not attend class as you choose.  However, if you come to class, please be prompt.  The classroom door is adjacent to the whiteboard and therefore it is extremely disruptive to the class if you come into the classroom after the start-of-class bell.  Please be seated in class by the time the start-of-class bell rings.  If a homework is due, please put it on the desk in the classroom prior to the star-of-class bell.

Textbook

• Ross Baldick, Applied Optimization: Formulation and Algorithms for Engineering Systems, Cambridge University Press 2006.  
• There is also a downloadable file of Appendices that includes pre-requisite material together with an Errata to the textbook and to the homework exercises.  (See Homework 0 for detailed instructions.)

Pre-requisites:

The class will assume some familiarity with concepts from real analysis such as sequences and limits, calculus, proofs, and will also assume familiarity with MATLAB. The mathematical pre-requisites for the class are contained in Appendix A of the course notes, which can be found at Appendices.  We will use the MATLAB Optiimization Toolbox extensively and you will need to have access to it, either on your own computer or through ECE resources.

Homework policy:

Homeworks will include problems from the textbook and will be assigned approximately once per week.  They include a mixture of theoretical work and the solution of problems, using graphical, analytical, and software techniques.  All homeworks must be done individually.  Each student must turn in an honest individual attempt. 

This course has a heavy homework load, with some very difficult problems, and I encourage you to discuss difficult homework problems both with classmates and with me in office hours.  However, copying of homeworks will not be tolerated.  If you are not prepared for a heavy homework load then this course is not for you! 

All homeworks must be turned in to pass the course, but late homeworks will be awarded a grade of zero unless permission for late submission is sought and given in advance of the due date.

Quiz and exam policy:

No make-up exams will be given.  Excused absence from a mid-term exam must be obtained in advance.  In this case, the student's final exam grade will be substituted for the missed exam.  In the case of an excused absence from the final exam, the course grade will be based on the homework and mid-term exam.  Unexcused absences from a mid-term or final will result in a grade of zero for that exam.  Excused absences from exams will be made only in extreme circumstance (serious illness, death in the immediate family, etc).  Requests for excused absences should be made in advance in writing and must be supported by appropriate documentation.

Exam dates:

• Mid-term: Thursday, March 6, in class,
• Final: time and location to be determined.

Grading policy:

A final score will be calculated based on:

• Homeworks 50%
• Mid-term 20%
• Final 30%

Homework 0:

Complete by the beginning of class on Tuesday, January 22.

1. Go to the instructor home page www.ece.utexas.edu/~baldick and look under "Teaching Plans and Course Web pages" for "Optimization of Engineering Systems." Download and print Appendices.
2. Read Appendix A. Confirm that you are familiar with at least 80% of the material in Appendix A. If you are not familiar with this material then you do not have the pre-requisites to take this course. I advise dropping the course if you are not familiar with at least 80% of the material in Appendix A.
3. Purchase the textbook and read chapters 1, 2, and 3.  We will only be covering these chapters briefly in class; however, there will be homework assigned from these chapters and you will be responsible for understanding the material in these chapters.

Homework 1:

Other information:

Allegations of Scholastic Dishonesty will be dealt with according to the procedures outlined in Appendix C, Chapter 11, of the General Information Bulletin, http://www.utexas.edu/student/registrar/catalogs/.

The University of Texas at Austin provides, upon request, appropriate academic adjustments for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4241 TDD, or the College of Engineering Director of Students with Disabilities, 471-4321.