Teaching Fall 2020 Math6350

Basic Information

Course: Math6350 Topics in Applied Math: First-order methods in optimization;

Section: 10;

Semester: Fall 2020;

Time: 08/31/20 - 12/12/20, T&R 02:20pm - 03:35pm;

Location: Remote Instruction (visit Blackboard to find Zoom link)

Instructor: Yanxiang Zhao, Phillips Hall 709

Phone: 202-994-0606

Email: yxzhao at email dot gwu dot edu

Office Hour: T&R 05:10pm--06:10pm or by appointment

Course Description

This course introduces state-of-the-art first order numerical methods in optimization. Some selected topics are: convex functions; conjugate functions; the proximal operator; primal and dual projected subgradient methods; mirror descent; proximal gradient methods.

Prerequisites

Linear algebra;
Numerical analysis;

Textbook

First-order methods in optimization by Amir Beck (main reference);
Introductory lectures on convex optimization by Y. Nesterov;
Conjugate duality and optimization by R. T. Rockafellar;
Convex optimization by S. Boyd and L. Vandenberghe.

Learning Outcomes

As a result of completing this course, the students will be able to:

understand the basic knowledges in optimization such as convexity, conjugacy, primal and dual relations;
Understand the first-order methods for optimization such as gradient descent, mirror descent, proximal gradient method etc.;
Apply the first-order methods to some real problems and implement them by Matlab.

Average minimum amount of independent, out-of-class, learning expected per week

More than 2/3 of the time you devote to this class should take place outside the classroom (lecture and recitation). Even the best students in the class should plan on spending an average of at least 6 hours a week on homework and other studying. Students who struggle with the material may need to spend more time in order to earn a grade they will find acceptable.

Calendar

	Mon	Tue	Wed	Thu	Fri
Week 1	Aug31	Sep01	Sep02	Sep03	Sep04
Week 2	Sep07	Sep08	Sep09	Sep10	Sep11
Week 3	Sep14	Sep15	Sep16	Sep17	Sep18
Week 4	Sep21	Sep22	Sep23	Sep24	Sep25
Week 5	Sep28	Sep29	Sep30	Oct01	Oct02
Week 6	Oct05	Oct06	Oct07	Oct08	Oct09
Week 7	Oct12	Oct13	Oct14	Oct15	Oct16
Week 8	Oct19	Oct20	Oct21	Oct22	Oct23
Week 9	Oct26	Oct27	Oct28	Oct29	Oct30
Week 10	Nov02	Nov03	Nov04	Nov05	Nov06
Week 11	Nov09	Nov10	Nov11	Nov12	Nov13
Week 12	Nov16	Nov17	Nov18	Nov19	Nov20
Week 13	Nov23	Nov24	Nov25	Nov26	Nov27
Week 14	Nov30	Dec01	Dec02	Dec03	Dec04
Week 15	Dec07	Dec08	Dec09	Dec10	Dec11
Week 16	Dec14	Dec15	Dec16	Dec17	Dec18

NOTE: In accordance with university policy, the final exam will be given during the final exam period and not the last week of the semester.

Homework

Homework 01
Homework 02
...

Exams

Oral midterm exam;
Oral final exam;

Grading

Your course grade will be determined by your cumulative average at the end of the term and will be based on the following scale:

	A	A-	B+	B	B-	C+	C	C-	D+	D	D-
scale	95%	90%	87%	83%	80%	77%	73%	70%	67%	63%	60%

Your cumulative average will be the following weighted average:

	Class performance	Midterm	Final
Scheme I	30%	30%	40%

Class Policies

University policy on Religious Holidays:

Students should notify faculty during the first week of the semester of their intention to be absent from class on their day(s) of religious observance;
Faculty should extend to these students the courtesy of absence without penalty on such occasions, including permission to make up examinations;
Faculty who intend to observe a religious holiday should arrange at the beginning of the semester to reschedule missed classes or to make other provisions for their course-related activities.

Academic Integrity

Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of other without crediting them and without appropriate authorization, and the fabrication of information. For the remainder of the code, see: http://www.gwu.edu/~ntegrity/code.html.

Support for Students Outside the Classroom

Disability Support Services (DSS): Any student who may need an accommodation based on the potential impact of a disability should contact the DSS office at 202-994-8250 in the Rome Hall, Suite 102, to establish eligibility and to coordinate reasonable accommodations. For additional information please refer to: http://gwired.gwu.edu/dss/.
University Counseling Center (UCC): The UCC (202-994-5300) offers 24/7 assistance and referral to address students' personal, social, career, and study skills problems. Services for students include: crisis and emergency mental health consultations; confidential assessment, counseling services (individual and small group), and referrals. For additional information please refer to: http://counselingcenter.gwu.edu/.

Security

In the case of an emergence, if at all possible, the class should shelter in place. If the buliding that the class is in is affected, follow the evacuation procedures for the building. After evacuation, see shelter at a predetermined rendezvous location.

Student Responsibilities and Classroom Courtesy:

You are responsible for knowing about all announcements made in class related to homework assignments, exams etc., and for all material covered in class.
Be aware of the University's Code of Academic Integrity, see http://www.gwu.edu/~ntegrity for details. If cases of academic dishonesty arise, whether on homeworks, quizzes or exams, they will be pursued to their conclusion.
Each student must conduct him or herself in a manner that promotes a positive atmosphere, conveys mutual respect, and creates no distractions, thereby allowing all students to focus on our goal: learning NUMERICAL ANALYSIS. In particular:
cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- cell phones, texting devices, laptops, and all other potentially distracting must be turned off during class;
- everyone should make a serious effort to arrive promptly for the start of class;
- except for serious reasons, once in class everyone should remain in class until the class is over;
- apart from the lecture, students asking the instructor questions, and students responding to the instructor's questions, the class should be silent.

Questions

Everyone is strongly encouraged to ask questions during class, and during office hours!

Library

Calculus (library call number: QA303.2 .S73 2016) is available on reserve as part of the Top Textbooks program at GW Libraries. Top Textbooks can be checked out for three hours at a time, can be taken outside the library, and have no cost to use.