MS&E 111X/211X: Introduction to Optimization, Fall 2019

Welcome to MS&E 111X/211X: Linear & Nonlinear Optimization, Fall 2019.

Piazza is now open This is a forum where students can post questions. I would prefer that any questions are directed to Piazza rather than the mailing list. Office hours will also be posted on Piazza.

Lectures: Tue, Thu 12:00 PM - 1:20 PM at Skillaud (is in the Skilling Building).

Problem session: Friday 4:30 PM - 5:20 PM at Skillaud. Give feedback here

Coursebook: Linear and Nonlinear Programming (LY 4th edition) by David Luenberger and Yinyu Ye.


  • Regular Students: HW 35%, Midterm 25% and Final 40%.

  • Project Students: HW 25%, Midterm 20%, Final 35% and Project 20% (updated).

  • No difference on taking 3 or 4 units.

Only project students (i.e. masters students) can take a project for a grade. You may join a project group if you are not a project student, but no extra credit will be given. There is no need to tell us in advanced whether you decide to do a project. We will only consider you a project student if you hand in a project by the deadline.

Course content: Optimization theory and modeling. The role of prices, duality, optimality conditions, and algorithms in finding and recognizing solutions. Perspectives: problem formulation, analytical theory, computational methods, and recent applications in engineering, finance, and economics. Theories: finite dimensional derivatives, convexity, optimality, duality, and sensitivity. Methods: simplex and interior-point, gradient, Newton, and barrier.

About optimization

Management Science & Engineering 211 is an introduction to Linear and Nonlinear Optimization intended primarily for master's degree students although qualified undergraduates and doctoral students are welcome. This course emphasizes data-driven modeling, theory and numerical algorithms for optimization with real variables. The field of optimization is concerned with the study of maximization and minimization of mathematical functions. Very often the arguments of (i.e., variables in) these functions are subject to side conditions or constraints. By virtue of its great utility in such diverse areas as applied science, engineering, economics, finance, health-care, and statistics, optimization holds an important place in the practical world and the scientific world. Indeed, as far back as the Eighteenth Century, the famous Swiss mathematician and physicist Leonhard Euler (1707-1783) proclaimed that … nothing at all takes place in the Universe in which some rule of maximum or minimum does not appear. The subject is so pervasive that we even find some optimization terms in our everyday language. Optimization often goes by the name Mathematical Programming. The latter name tends to be used in conjunction with finite-dimensional optimization problems, which in fact are what we shall be studying here. The word “Programming” should not be confused with computer programming which in fact it antedates. As originally used, the term refers to the timing and magnitude of actions to be carried out so as to achieve a goal in the best possible way.


MS&E 211 requires no prior course in optimization, but it does have just one prerequisite: Mathematics 51 (Linear algebra & multivariate differential calculus) or equivalent. This means that students should, at the very least, be familiar with the concept of a finite dimensional vector space, most importantly Rn (real n-space), the algebraic manipulation of vectors and matrices, the property of linear independence of vectors, elimination methods for solving systems of linear equations in many variables, the elementary handling of inequalities, and a good grasp of such analytic concepts as continuity, differentiability, the gradient, and the Hessian matrix.

Final exam and midterm

Exams and mid-terms will be open book and lecture notes, but no electronics devices will be allowed (except a basic calculator).

The mid-term will be in class, on Tuesday November the 7th.

The final exam will be 12:15-3:15 p.m, on Thursday December 14th.

Please post on piazza under ‘logistics’ if any of these dates do not work for you and will setup an alternative time.


There will be a required project for those students taking this course as a project-course. We will distribute the project description on the fourth week. The grades for project and non-project students will be graded separately.

Project groups can contain at most three people.

The projects will be due Friday the 8th of December at 5pm (submit the project as you would submit a HW).

Other courses in optimization

The MS&E Department has several other courses in optimization and related topics. Those focusing primarily on optimization as such are:

MS&E 111 (=E62), 212, 310, 311, 312, 313.

Courses emphasizing applied settings in which optimization plays a major role are:

MS&E 251, 302, 322, 339, 334, 344, 351, 361.

For descriptions of the content of these courses, as well as those in other departments, consult explore courses.


Q: What is the difference between MS&E 211X and MS&E 211?

The accelerated version assumes students have a linear algebra and multivariate calculus background whereas the non-accelerated version does not. Consequently, the former course moves at a faster pace.

Q: I am an on-campus student, how do I login to view my course lectures?

A: Stanford students attending graduate classes on-campus should visit Valid SUNet ID required.

Q: I am enrolled through SCPD, how do I login to view my course lectures?

A: Please log into your mystanfordconnection account at For login issues please contact technical support,

Q: What is a problem session?

A: In addition to our office hours, there will be a ‘‘problem session’’ on most Fridays. This problem session will review lecture topics of each week, and would show you homework samples and their solutions; and they will be video taped as well.

Q: What is a remote student?

A: Remote students are students that are (i) non-SCPD and (ii) off campus for some (or all) of the quarter. For exams and midterm and final exam it is important that remote students organize a proctor ahead of time. More details on this will be released during the first week of class.

Information for Students with Documented Disabilities

Students who have a disability which may necessitate an academic accommodation or the use of auxiliary aids and services in a class, must initiate the request with the Student Disability Resource Center (SDRC), located within the Office of Accessible Education (OAE). The SDRC will evaluate the request with required documentation, recommend appropriate accommodations, and prepare a verification letter dated in the current academic term in which the request is being made. Please contact the SDRC as soon as possible; timely notice is needed to arrange for appropriate accommodations. The Office of Accessible Education is located at 563 Salvatierra Walk (phone: 723-1066; TDD: 725-1067).