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EE563 Convex Optimization

Spring 2020

Department of Electrical Engineering
Syed Babar Ali School of Science and Engineering
Lahore University of Management Sciences.



Course Overview

In this course, we will focus on the convex optimization theory, applications and algorithms. We will cover the topics: convex sets and functions, convex optimization problems, applications of convex optimization in wireless communications, signal processing, machine learning and big data, concept of duality and brief overview of algorithms (Newton, interior point methods).

Optimization has wide-ranging applications in diverse fields of science and engineering. We will focus on maintaining a balance between applications and theory to enable the students to recognize, formulate and solve a convex problem.

Final Exam

Announcements

  • (Apr. 03) We will switch to online learning due to Covid-19

  • (Feb. 19) Assignment 02 has been posted. It is due on Mar. 02.

  • (Jan. 28) Assignment 01 and Reading Assignment have been posted. Assignment 1 is due Feb. 12.

  • (Jan. 19) Welcome to EE563. Course outline has been posted.

Administrative Details

  • Course Outline (Click to download)

  • Textbook:

  • Supplementary Reading:

    • Introduction to Linear Optimization, by Bertsimas and Tsitsiklis

  • Office Hours and Contact Information

    • Instructor (zubair.khalid@lums.edu.pk): Monday and Wednesday, 3-5 pm

Grading Distribution

  • Assignments, 25 %

  • Quizzes, 10 %

  • Mid-Exam, 20 %

  • Mid-Exam, 20 %

  • Final Exam, 25 %

Lecture Notes and Exams

Lecture notes, exams and reading assignmnets will be posted here.

Assignments

Assignment Due Date Solutions
Assignment 01 Feb. 12 Solutions
Assignment 02 Mar. 02 Solutions
Assignment 03 Mar. 02 Solutions
Assignment 04 May. 03 Solutions
Assignment 05 May. 12 Solutions

Tutorials

Quizzes

Quiz Solutions
Quiz 01 Solutions
Quiz 02 Solutions
Quiz 03 Solutions
Quiz 04 Solutions
Quiz 05 Solutions

Lecture Plan

  • Lecture 01

    • Course Introduction

    • Fundamental concepts

  • Lecture 02

    • Linear Algebra Review

  • Lecture 03

    • Linear Algebra Review

    • Convex Sets, Affine Sets, Hyperplane, Halfspaces

  • Lecture 04

    • Convex Sets, Balls, Cones, Convexity preseving operations on sets

  • Lecture 05

    • Generalized inequalities, Minimum and minimal elements, Dual cones

  • Lecture 06

    • Convex Functions, First-oder and second-order conditions

  • Lecture 07

    • Examples of convex functions, Connection between convex functions and convex sets

  • Lecture 08

    • Revisit Jensen inequality, Convexity preserveing operations

  • Lecture 09

    • Conjugate function, Quasiconvex functions, Log-concave functions, K-Convexity

  • Lecture 11

    • Optimization Application: Beamforming for SNR maximization, Interference suppression and SINR maximization

  • Lecture 12

    • Optimization Application: Robust Beamforming. Optimization Problems Notation and Equivalent Formulation

  • Lecture 13

    • Mid-Exam 1

  • Lecture 14

    • Optimization Problem Formulation, Equivalent Problems, Linear Program, LP Interpretation

  • Lecture 15

    • Application Examples of LP, Introduction to CVX

Online Modules