The official course title is "Introduction to Optimization Theory". However, we will try to split our time evenly between applications/modeling, theory, and methods.
Mathematical optimization is the science of finding the best (e.g. lowest cost) solution to a problem. Often, we also try to prove that it is the best, or that it is within some small percentage of the best solution. Some common examples are:
An introduction to various aspects of optimization theory, including linear and nonlinear programming, primal dual methods, calculus of variations, optimal control theory, sensitivity analysis and numerical methods.
Follow-up courses: Math 436 Numerical Analysis, Math 419/519 Stochastic Math Models, various statistics classes.
Related courses:
Class meetings will be mostly interactive lectures and computer lab work, with some time to discuss homework.
Mon/Wed:
11:30-12:30 Office hours
12:30- 1:20 Math 121 in Pray-Harrold 202
1:20- 2:20 Office hours
Tue/Thu:
11:30-12:30 Office hours in my office
12:30- 1:20 Math 121 in Pray-Harrold 202
1:20- 2:00 Office hours in PH 202, proceeding to PH 520
2:00- 3:15 Math 319 in Pray-Harrold 520
3:15- 4:00 Office hours in PH 520
4:00- 5:15 Math 560 in Pray-Harrold 520
Fri:
No official office hours, but I'm often on campus.
E-mail me to make an appointment, or drop by.
I am also happy to make appointments if you cannot come to the general office hours. Please send me e-mail to arrange an appointment.
I am definitely unavailable during the times I teach other classes:Many assignments in this course will be in the form of papers, which I want to be well written. Please consult with The Writing Center for help in tuning up your writing.
Our suggested (not required!) textbook is "Operations Research: Applications and Algorithms (4th revised edition)" by Wayne Winston (2004), retail price around $161 (yikes!) The price is why it's suggested but not required. My copy of the book has around 1400 pages (!). I understand that some students like to order international copies, which may have a different number of pages. I would be very suspicious of anything with less than, say, 1000 pages.
I will also be asking for your feedback at the end of many class meetings, written on a 3-by-5 inch notecard. Please pick up a pack of them (at least 25 cards); this should cost about a dollar.
We will also be using software. At least one of the following, and possibly more, is required:
We will use the EMU-Online system. You are expected to keep an eye on your scores using the system, and get extra help if your scores indicate the need.
Our primary goal is to teach you to be a good (or great!) optimizer. To be a good optimizer, you need:
Preliminaries 3 basic models: the diet problem (LP), pricing and production (NLP), shift scheduling (IP) Intro to Excel/Gnumeric and Matlab/Octave/Scilab convexity and concavity of sets and functions in multiple dimensions networks/graph theory concepts LP Common models: diet production planning blending network flows (min cost, max flow, shortest path) Software solutions (Excel/Gnumeric, Matlab/Octave/Scilab) Sensitivity analysis (experimental, not formula-based) Geometry of LPs NLP Linear algebra review: quadratic forms, eigenvalues/vectors Common models: L2 (least-squares) regression maximum likelihood estimators (MLEs) solving differential equations many others Software solutions (Excel/Gnumeric, Matlab/Octave/Scilab) Geometry of NLPs Solution methods for unconstrained problems Solution methods for constrained problems IP Common models: shift scheduling knapsack problems assignment problems travelling salesperson (TSP) vehicle routing problem (VRP) set covering/partitioning/packing Binary Variable techniques: fixed-cost problems Solution via branch-and-bound Cutting Planes More LP: L1 or L-infinity regression; Compressive Sensing? Solution via Simplex Method Duality/Sensitivity Analysis (formula-based) Solution via Interior Point Methods Heuristic Methods (if any time remains) Simulated Annealing Genetic Algorithms Tabu search Biomimic Algorithms (Ant-colony, etc) Dynamic Programming (if any time remains)
Regular attendance is strongly recommended. There will be material presented in class that is not in the textbook, yet will be very useful. Similarly, there are things in the textbook that are might not be covered in class, but are still very useful. If you must miss a class, arrange to get a copy of the notes from someone, and arrange for someone to ask your questions for you.
My lectures and discussions mostly use the chalkboard, along with demonstrations in Excel and other mathematical software. I do not usually have PowerPoint-like presentations, and thus cannot hand out copies of slides.
Homework will be assigned about once a week. It will sometimes be a small problem set designed to help you understand the behavior of math models. Other times, it will involve writing up a little paper on an assigned topic. All homework should be typed.
Homework papers should be submitted on-line, where they might be checked by TurnItIn.com or a similar service. This is partly to help keep you honest, and partly to help you learn acceptable ways to cite the work of others. A side benefit is that sometimes TurnItIn finds papers relevant to your work that you would not have found otherwise!
There will be no exams, unless the class demonstrates an unwillingness to be motivated any other way.
Instead of exams, we will have two projects. Your results for each will reported in a paper and a presentation to the class. You may work by yourself or in a team of 2 people, but no groups larger than 2 will be allowed. You may switch project partners at your will. Your project grades will each be split into roughly: 10 percent for the project proposal (due 2 weeks before the project), 80 percent for the written paper and actual work, and 10 percent for the presentation (subject to change). The presentations for the second project will be made during the time slot reserved for the final exam.
No scores will be dropped, unless a valid medical excuse with evidence is given. In the unfortunate event of a medical need, the appropriate grade or grades may be dropped entirely (at the professor's discretion), rather than giving a make-up. You are highly encouraged to still complete the relevant assignments and consult with me during office hours to ensure you know the material.
Your final score will be computed as follows:I support students' right to observe religious holidays without penalty. To the best of my ability, I will schedule exams to not conflict with major religions' holidays. Students are to provide advance notice to the instructor in order to make up work, including examinations that they miss as a result of their absence from class due to observance of religious holidays. If satisfactory arrangements cannot be made, the student may appeal to the head of the department.
Academic dishonesty, including all forms of cheating and/or plagiarism, will not be tolerated in this class. Penalties for an act of academic dishonesty may range from receiving a failing grade for a particular assignment to receiving a failing grade for the entire course. In addition, you may be referred to the Office of Student Judicial Services for discipline that can result in either a suspension or permanent dismissal. The Student Conduct Code contains detailed definitions of what constitutes academic dishonesty, but if you are not sure about whether something you’re doing would be considered academic dishonesty, consult with the instructor.
Students are expected to abide by the Student Conduct Code and assist in creating an environment that is conducive to learning and protects the rights of all members of the University community. Incivility and disruptive behavior will not be tolerated and may result in a request to leave class and referral to the Office of Student Judicial Services (SJS) for discipline. Examples of inappropriate classroom conduct include repeatedly arriving late to class, using a cellular telephone, or talking while others are speaking. You may access the Code online at www.emich.edu/sjs.
If you wish to be accommodated for your disability, EMU Board of Regents policy #8.3 requires that you first register with the Access Services Office (ASO) in room 203 King Hall. You may contact ASO by telephone at (734) 487-2470. Students with disabilities are encouraged to register with ASO promptly as you will only be accommodated from the date you register with them forward. No retroactive accommodations are possible.