Optimization consists of finding the best feasible selection amongst competing alternatives. Optimization methods are used in a wide range of applications including:
There is no one optimization algorithm to rule them all, so in this class we will learn about several different classes of algorithms. You will learn the strengths and limitations of different approaches, and how to frame your analysis in a way that is “optimization-friendly”. Optimization almost always involves complicated tradeoffs, and computers are useful in managing this complexity and extracting insight.
This course assumes no prior exposure to optimization, but you will need a foundation in mathematics and scientific programming. Appendix A of our textbook reviews some key mathematical concepts if you are in need of a refresher.
It doesn’t matter what programming language you have experience with as long as you are reasonably comfortable. Most students in the class complete assignments in Matlab, Python, or Julia. You should be familiar with the fundamentals: functions, loops, conditionals, variable types, arrays (vectors), use of numerical libraries. Familiarity with things like object oriented programming is not needed.
Definitely. Many undergraduates elect to take this course and do very well (based on past semesters the average undergraduate and graduate grades are statistically identical). However, keep in mind that this is a graduate course and expectations will be consistent with graduate-level work. Also, the course project is often, but not always, most effective when applied to an ongoing research project.
As compared to an undergraduate class:
A colleague and I have written a textbook that you can download (linked on Schedule). We are under contract with Cambridge University Press—the printed version should be available this coming Fall.
Research suggests that you learn more deeply if you wrestle with the concepts before you learn the “right way” to think about them. Thus, I try to orient classes around self-discovery and recommend that you wait to read the textbook until after lectures. I will ask you to predict things, try to solve problems in class, discuss concepts with your neighbor, etc. This type of interaction doesn’t work well in virtual settings with large groups, and our class size is too large to all meet in person given current COVID-19 restrictions.
To facilitate deep learning we will use a hybrid approach where you will:
There are six homeworks designed to teach the important concepts in the class and to help you succeed on your project and future optimization problems. Each homework is like a miniature project with a memo spanning a two-week period. Each homework is assigned two weeks before the deadline because it is designed to take that long. If you put off most of the work until a few days before the deadline you will not be as successful. Homework will typically be due Wednesday at midnight (actually 11:59pm) via Learning Suite. The intent of the memo format is that you will learn deeper by having to explain in words, it will better prepare you for the type of work you will have in an engineering career, and the hard work you did will be much more accessible to you when referring to it later. There is no need to write lengthy narratives, but a few sentences here and there can go a long ways in providing clarity.
Homework must be submitted as a PDF. There is no specific requirement on format. The goal is to be clear about your work. A series of numbers and plots is insufficient. For each problem you should detail assumptions and methodology if applicable, clearly explain your results, and briefly discuss their significance and limitations. Imagine your audience to be a colleague or supervisor—someone who understands your field but is not necessarily familiar with the details of your particular problem.
You will also need to submit any source code that you developed. You should not include source code directly in your report, but you may refer to it from your report if necessary. Source code should be commented so that it is easily readable. Each submission should consist of one PDF file for the report and one zipped directory containing any auxiliary material (e.g., source code).
Late homework will be accepted with a penalty of 20% per day. Last minute issues often happen in life so be sure to start early! Despite your best planning you will likely have an unexpected event, obligation, or illness pop up. To help with this, I will give you three free late days (total per semester, not per assignment). This policy is designed to help with unexpected issues so please don’t ask for homework extensions or other exceptions (unless you have an extreme or extended event like a hospitalization or death in the family).
Working with others on homework is definitely encouraged, but you must do your own work and write-ups. Referring to solution manuals or student work from previous years is a violation of department policy and the honor code.
The main thrust of this course is a semester-long project that will allow you to dive deeper into an area or application that you are interested in. The project is open-ended and you will work in small groups of size 1-3. At the end of the semester you will give a presentation on your project.
Your project may be aligned with research you are doing outside of the classroom (in fact I recommend doing so if applicable). The milestones within the project will consist of a one paragraph overview of your idea early in the semester, a two-page executive summary describing the methodology and any results about a month before the end of the semester, and a final presentation during the last week of class. More details on the project are found here. Example project reports from past classes can be found on the Resources page. Note that these are a different format (report instead of a presentation).
As mentioned, there will be weekly quizzes to help you gauge understanding and reinforce concepts. Quizzes may also ask about participation with in-class exercises. Schedule a reminder because we won’t open up late quizzes after they are due (it becomes a logistical pain that isn’t justifiable giving the small number of points). Instead, I will drop two quizzes because we all forget or have emergencies occasionally.
There are no midterms but there will be a comprehensive final exam.
In keeping with the principles of the BYU Honor Code, students are expected to be honest in all of their academic work. Academic honesty means, most fundamentally, that any work you present as your own must in fact be your own work and not that of another. Violations of this principle may result in a failing grade in the course and additional disciplinary action by the university. Students are also expected to adhere to the Dress and Grooming Standards. Adherence demonstrates respect for yourself and others and ensures an effective learning and working environment. It is the university’s expectation, and every instructor’s expectation in class, that each student will abide by all Honor Code standards. Please call the Honor Code Office at 422-2847 if you have questions about those standards.
As part of an overall teaching/learning approach to aid student learning, the course instructor may make available to students solutions to some prior coursework. However, outside of this appropriate usage, relying on and/or copying solutions (obtained online or from any source) to assigned coursework represents a clear example of turning in work that is not your own.
All course materials (e.g., outlines, handouts, syllabi, exams, quizzes, PowerPoint presentations, lectures, audio and video recordings, etc.) are proprietary. Students are prohibited from posting or selling any such course materials without the express written permission of the professor teaching this course. To do so is a violation of the Brigham Young University Honor Code.
In accordance with Title IX of the Education Amendments of 1972, Brigham Young University prohibits unlawful sex discrimination against any participant in its education programs or activities. The university also prohibits sexual harassment-including sexual violence-committed by or against students, university employees, and visitors to campus. As outlined in university policy, sexual harassment, dating violence, domestic violence, sexual assault, and stalking are considered forms of “Sexual Misconduct” prohibited by the university.
University policy requires all university employees in a teaching, managerial, or supervisory role to report all incidents of Sexual Misconduct that come to their attention in any way, including but not limited to face-to-face conversations, a written class assignment or paper, class discussion, email, text, or social media post. Incidents of Sexual Misconduct should be reported to the Title IX Coordinator at t9coordinator@byu.edu or (801) 422-8692. Reports may also be submitted through EthicsPoint at https://titleix.byu.edu/report or 1-888-238-1062 (24-hours a day).
BYU offers confidential resources for those affected by Sexual Misconduct, including the university’s Victim Advocate, as well as a number of non-confidential resources and services that may be helpful. Additional information about Title IX, the university’s Sexual Misconduct Policy, reporting requirements, and resources can be found at http://titleix.byu.edu or by contacting the university’s Title IX Coordinator.
Brigham Young University is committed to providing a working and learning atmosphere that reasonably accommodates qualified persons with disabilities. If you have any disability which may impair your ability to complete this course successfully, please contact the University Accessibility Center (UAC), 2170 WSC or 422-2767. Reasonable academic accommodations are reviewed for all students who have qualified, documented disabilities. The UAC can also assess students for learning, attention, and emotional concerns. Services are coordinated with the student and instructor by the UAC. If you need assistance or if you feel you have been unlawfully discriminated against on the basis of disability, you may seek resolution through established grievance policy and procedures by contacting the Equal Employment Office at 422-5895, D-285 ASB.
“Sadly, from time to time, we do hear reports of those who are at best insensitive and at worst insulting in their comments to and about others… We hear derogatory and sometimes even defamatory comments about those with different political, athletic, or ethnic views or experiences. Such behavior is completely out of place at BYU, and I enlist the aid of all to monitor carefully and, if necessary, correct any such that might occur here, however inadvertent or unintentional. “I worry particularly about demeaning comments made about the career or major choices of women or men either directly or about members of the BYU community generally. We must remember that personal agency is a fundamental principle and that none of us has the right or option to criticize the lawful choices of another.” President Cecil O. Samuelson, Annual University Conference, August 24, 2010 “Occasionally, we … hear reports that our female faculty feel disrespected, especially by students, for choosing to work at BYU, even though each one has been approved by the BYU Board of Trustees. Brothers and sisters, these things ought not to be. Not here. Not at a university that shares a constitution with the School of the Prophets.” Vice President John S. Tanner, Annual University Conference, August 24, 2010
Brigham Young University’s devotional and forum assemblies are an important part of your BYU experience. President Cecil O. Samuelson said, “We have special and enlightening series of devotional and forum assemblies…that will complement, supplement, and enrich what will also be a very productive period in your classrooms, laboratories, and libraries. We look forward to being with you each Tuesday…and hope that you will regularly attend and bring your friends and associates with you…A large part of what constitutes the unique ‘BYU experience’ is found in these gatherings where the Spirit has been invited and where we have the opportunity to discuss and consider things of ultimate worth and importance that are not afforded to the academic community on almost any other campus” (from the address “The Legacy of Learning”, 30 August, 2005). Your attendance at each forum and devotional is strongly encouraged.
Mental health concerns and stressful life events can affect students’ academic performance and quality of life. BYU Counseling and Psychological Services (CAPS, 1500 WSC, 801-422-3035, caps.byu.edu) provides individual, couples, and group counseling, as well as stress management services. These services are confidential and are provided by the university at no cost for full-time students. For general information please visit https://caps.byu.edu; for more immediate concerns please visit http://help.byu.edu.
The first injunction of the Honor Code is the call to “be honest.” Students come to the university not only to improve their minds, gain knowledge, and develop skills that will assist them in their life’s work, but also to build character. “President David O. McKay taught that character is the highest aim of education” (The Aims of a BYU Education, p.6). It is the purpose of the BYU Academic Honesty Policy to assist in fulfilling that aim. BYU students should seek to be totally honest in their dealings with others. They should complete their own work and be evaluated based upon that work. They should avoid academic dishonesty and misconduct in all its forms, including but not limited to plagiarism, fabrication or falsification, cheating, and other academic misconduct.
Intentional plagiarism is a form of intellectual theft that violates widely recognized principles of academic integrity as well as the Honor Code. Such plagiarism may subject the student to appropriate disciplinary action administered through the university Honor Code Office, in addition to academic sanctions that may be applied by an instructor. Inadvertent plagiarism, which may not be a violation of the Honor Code, is nevertheless a form of intellectual carelessness that is unacceptable in the academic community. Plagiarism of any kind is completely contrary to the established practices of higher education where all members of the university are expected to acknowledge the original intellectual work of others that is included in their own work. In some cases, plagiarism may also involve violations of copyright law. Intentional Plagiarism-Intentional plagiarism is the deliberate act of representing the words, ideas, or data of another as one’s own without providing proper attribution to the author through quotation, reference, or footnote. Inadvertent Plagiarism-Inadvertent plagiarism involves the inappropriate, but non-deliberate, use of another’s words, ideas, or data without proper attribution. Inadvertent plagiarism usually results from an ignorant failure to follow established rules for documenting sources or from simply not being sufficiently careful in research and writing. Although not a violation of the Honor Code, inadvertent plagiarism is a form of academic misconduct for which an instructor can impose appropriate academic sanctions. Students who are in doubt as to whether they are providing proper attribution have the responsibility to consult with their instructor and obtain guidance. Examples of plagiarism include: Direct Plagiarism-The verbatim copying of an original source without acknowledging the source. Paraphrased Plagiarism-The paraphrasing, without acknowledgement, of ideas from another that the reader might mistake for the author’s own. Plagiarism Mosaic-The borrowing of words, ideas, or data from an original source and blending this original material with one’s own without acknowledging the source. Insufficient Acknowledgement-The partial or incomplete attribution of words, ideas, or data from an original source. Plagiarism may occur with respect to unpublished as well as published material. Copying another student’s work and submitting it as one’s own individual work without proper attribution is a serious form of plagiarism.