625.615.81 - Introduction to Optimization

Applied and Computational Mathematics
Spring 2024


This course introduces applications and algorithms for linear, network, integer, and nonlinear optimization. Topics include the primal and dual simplex methods, network flow algorithms, branch and bound, interior point methods, Newton and quasi-Newton methods, and heuristic methods. Students will gain experience in formulating models and implementing algorithms using MATLAB. No previous experience with the software is required. Prerequisite(s): Multivariate calculus, linear algebra. Comfort with reading and writing mathematical proofs would be helpful but is not required. Course Note(s): Due to overlap in subject matter in EN.625.615 and EN.625.616, students may not receive credit towards the MS or post-master’s certificate for both EN.625.615 and EN.625.616.


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Paul Nicholas


Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the left menu in Canvas. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged topreview all sections of the module before starting. Most modules run for a period of seven (7) days, except as noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

The following topics are covered in this course (subject to change):

Course Goals

This course covers fundamental methods of optimization. Emphasis in this course will be on formulating optimization problems, understanding the methods available to address them, and solving them using appropriate means.

Course Learning Outcomes (CLOs)



Rao, Singiresu S. (2009). Engineering Optimization: Theory and Practice (5th ed.). Hoboken, NJ: John Wiley & Sons, Inc. ISBN-13:978-1119454717

Textbook information for this course is available online through the appropriate bookstore website. For online courses, search the MBS website.


Additionally, the following text or other texts that you may have from previous courses may be useful for this course if you find yourself struggling with specific skills:

Bronson, Richard and Govindasami Naadimuthu (1997). Schaum’s Outline of Theory and Problems of Operations Research (2nd ed.).New York, NY: McGraw-Hill.

Required Software

You will need access to a recent version of MATLAB with the Optimization Toolkit. The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Send an email to software@jhu.edu to request your license file/code. Please indicate that you need a standalone file/code. You will need to provide your first and last name, as well as your Hopkins email address. You will receive an email from Mathworks with instructions to create a Mathworks account. The MATLAB software will be available for download from the Mathworks site.

Student Coursework Requirements

It is expected that each module will take approximately 8–11 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 2–3 hours per week), and writing assignments (approximately 4–5 hours per week).

This course will consist of the following basic student requirements:

Preparation and Participation (10% of Final Grade Calculation)

You are responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are fromthe course text. Additional reading may be assigned to supplement text readings.

Post your initial response to the discussion questions by the evening of day 6 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., timeliness). 

Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (i.e., critical thinking). Just posting your response to a discussion question is not sufficient; I want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I will monitor module discussions and will respond to some of the discussions as discussions are posted. Evaluation of preparation and participation is based on contribution to discussions.

Preparation and participation are evaluated by the following grading elements:

Preparation and participation is graded as follows:

100–90 = A—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion];Critical Thinking [rich in content; full of thoughts, insight, and analysis].

89–80 = B—Timeliness [frequently participates; all required postings; some not in time for others to read and respond];Critical Thinking [substantial information; thought, insight, and analysis has taken place].

79–70 = C—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace].

<70 = F—Timeliness [rarely participates; some, or all required postings missing]; Critical Thinking [rudimentary and superficial; no analysis or insight is displayed].

Assignments (30% of Final Grade Calculation)

All modules, except Modules 7 and 14, will contain a graded problem set. These assignments will be based on the theory and algorithms discussed in the associated module. Each assignment will have approximately 4 problems of varying difficulty. You are encouraged to collaborate (within the JHU guidelines on academic integrity) on these assignments but you should write up your own final solution. Direct copying of someone else’s written work or computer code is considered to be cheating and will not be tolerated.

Usually you will be required to complete a problem “by hand.” This means that you should not use any software or electronic device (save a simple calculator) to do the work. (However there is no reason you cannot check your work with commercially available software, shareware, freeware, etc.) Some assignments will have a computing (MATLAB) component that you will also complete individually.

Graded assignments will be returned weekly, providing frequent feedback. Problem sets will be graded out of 60 points. The allocation of those points to specific problems may vary from assignment to assignment depending on the degree of difficulty. Partial credit may be given. For each individual graded item, the following (approximate) rubric will be used:

All problem sets are due according to the dates in the Calendar. No late problem sets will be accepted without prior approval.

Exams (60% of Final Grade Calculation, combined from 30% for Midterm and 30% for Final)

There will be two exams given, one in Module 7 and the other in Module 14. Each of these exams will be timed and open book, with no collaboration allowed. The midterm exam (Module 7) will focus on the course material taught in Modules 1-6. The final exam (Module 14) will focus on the course material taught in Modules 8-13.

Both of these exams will provide you the opportunity to demonstrate your ability to determine the required techniques and apply them to solve an optimization problem outside of the framework of a specific lecture/individual topic. Each of these exams will be worth 30% of your final grade.

For each individual graded item, the following (approximate) rubric will be used:

Grading Policy

Assignments and Exams are due according to the dates posted in the Canvas course site. You may check these due dates in the Course Calendar. Grades will be posted one week after assignment due dates. Graded work (with the exception of the final exam) will be returned to the student for review.

I generally do not directly grade spelling and grammar. However, egregious violations of the rules of the English language will be noted without comment. Consistently poor performance in either spelling or grammar is taken as an indication of poor written communication ability that may detract from your grade.

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will be posted no later than one week after assignment due dates.

The ability to clearly communicate results is an important component of this field of analysis. Egregious violations of the rules of theEnglish language, and/or incomprehensible explanations will result in a reduced grade.

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10). For all graded assignments, the following grading standards apply. A grade of A-/A/A+ indicates achievement of consistent excellence and distinction throughout the course; that is, conspicuous excellence in all aspects of assignments. A grade of B-/B/B+ indicates work that meets all course requirements on a level appropriate for graduate academic work. A grade of less than B- indicates the student is not performing at a level expected of a graduate student.

These criteria apply to both undergraduates and graduate students taking the course.

Score RangeLetter Grade
100-98= A+
97-94= A
93-90= A−
89-87= B+
86-83= B
82-80= B−
79-77= C+
76-73= C
72-70= C−
69-67= D+
66-63= D
<63= F

Final grades will be determined by the following weighting:


% of Grade

Preparation and Participation




Exams (midterm + final)

60% (30% + 30%)

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.