ELEC-E5424 - Convex optimization D, Lecture, 6.9.2023-14.12.2023

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  Schedule

  	Lectures (Wed. 9.15-11:00)		Exercises (Thu. 12:15-14:00)
  13.9	Lect. 1: T3 Computer Science build.	14.9	Lect. 2/Exer.: TU7 Maarintie 8
  20.9	Lect. 3: T3 Computer Science build.	21.9	Lect. 4/Exer.: TU7 Maarintie 8
  27.9	Lect. 5: T3 Computer Science build.	28.9	Lect. 6/Exer.: TU7 Maarintie 8
  4.10	Lect. 7: T3 Computer Science build.
  11.10	Lect. 8: T3 Computer Science build.	12.10	Exer. 1: TU7 Maarintie 8
  	Exam week (no teaching)		Exam week (no teaching)
  25.10	Lect. 9: T3 Computer Science build.	26.10	Lect. 10/Exer.: TU7 Maarintie 8
  1.11	Lect. 11: T3 Computer Science buil.	2.11	Exer. 2: TU7 Maarintie 8
  8.11	Lect. 12: T3 Computer Science buil.
  15.11	Lect. 13: T3 Computer Science buil.	16.11	Exer. 3: TU7 Maarintie 8
  22.11	Lect. 14: T3 Computer Science buil.
  29.11	Exer. 4: T3 Computer Science build.
  	Preparation week		Preparation week
  13.12	Exam (9:00-11:00): T3

  
  

  Textbook and Optional References

  •        Stephen Boyd; Lieven Vandenberghe, Convex Optimization (Textbook!)

  •        Ben-Tal and A. Nemirovski, Lectures on Modern Convex Optimization: Analysis, Algorithms, and Engineering Applications

  •        Y. Nesterov, Introductory Lectures on Convex Optimization: A Basic Course

  •        J. Gallier and J. Quaintance, Algebra, Topology, Differential Calculus, and Optimization Theory For Computer Science and Engineering

  Course Requirements and Grading

  Requirements:

  •        4 homework assignments. Homeworks will normally be assigned on Wendsdays and will be due in 2 weeks.

  •        Final Exam. The format will be decided depending on the sitation.

  Grading: 

  Homeworks: 60%. Exam: 40%. These weights are approximate. We reserve the right to change them later. Can be also discussed.

  Description

  Concentrates on recognizing and solving (using standard packages) convex optimization problems that arise in practice!

  •        Convex sets, functions, and optimization problems.

  •        Least-squares, linear and quadratic programs.

  •        Semidefinite programming (SDP).

  •        Minimax, extremal volume, and other problems with geometric interpretation.

  •        Optimality conditions, duality theory, theorem of alternatives.

  •        Introduction to unconstrained optimization algorithms.

  •        Introduction to interior-point methods for constrained optimization.

  •        Applications.

  Course Objectives

  •        to give the tools and training to recognize convex optimization problems that arise in electrical engineering and computer science

  •        to present the basic theory of such problems, concentrating on results that are useful in computations

  •        to give a thorough understanding of how such problems are solved, and some experience in solving them

  •        to give the background required to use the standard methods and software packages (CVX toolbox) in your own research work

  •        to give a number of examples of successful application of convex optimization techniques for solving problem in applied mathematics, computer science, statistics, electrical engineering, and science and engineering in general

  
  

  • Valitse aktiviteetti Announcements

    

    Announcements Keskustelualue
  • Valitse aktiviteetti Introduction and Overview

    

    Introduction and Overview Tiedosto PDF

    What the course is about

  • Valitse aktiviteetti Useful Concepts and Facts from Linear Algebra

    

    Useful Concepts and Facts from Linear Algebra Tiedosto PDF

    Some concepts from linear algebra that are heavily used in the textbook for the course and in general in convex optimization.

  • Valitse aktiviteetti Convex Sets

    

    Convex Sets Tiedosto PDF

    subspace, afiine set, convex set, convex cone (simple examples and properties)

    combination and hulls
    

    ellipsoids, polyhedra, norm balls
    

    affine and projective transformations
    

    separating hyperplanes
    

    generalized inequalities
    

  • Valitse aktiviteetti Convex Functions

    

    Convex Functions Tiedosto PDF

    convex functions, epigraph (simple examples, elementary properties)

    more examples, more properties
    

    Jensen's inequality
    

    quasiconvex, quasiconcave functions
    

    log-convex and log-concave functions
    

    K-convexity
    

  • Valitse aktiviteetti Convex Optimization Problems

    

    Convex Optimization Problems Tiedosto PDF

    abstract form problem

    standard form problem

    convex optimization problem
    

    standard form with generalized inequalities
    

    mulitcriterion optimization
    

    restriction and relaxation
    

  • Valitse aktiviteetti Linear and Quadratic Problems, Semidefinite Programming (SDP) Format

    

    Linear and Quadratic Problems, Semidefinite Programming (SDP) Format Tiedosto PDF

    linear programming (examples and applications)

    linear fractional programming 

    quadratic optimization problems 

    (quadratically constrained) quadratic programming 

    examples and applications 

    Semidefinite programming 

    applications

  • Valitse aktiviteetti CVX Tutorial

    

    CVX Tutorial Tiedosto PDF

    How to use solvers to solve convex optimization problems

  • Valitse aktiviteetti Duality

    

    Duality Tiedosto PDF

    Lagrange dual function

    Lagrange dual problem

    strong duality and Slater's condition

    KKT optimality conditions

    sensitivity analysis

    duality in generalized inequalities notation

    theorem of alternatives

  • Valitse aktiviteetti Smooth Unconstrained Minimization Algorithms

    

    Smooth Unconstrained Minimization Algorithms Tiedosto PDF

    terminology

    general descent method

    line search types

    gradient method

    steepest descent method

    Newton's method

  • Valitse aktiviteetti Introduction to Sequential Unconstrained Minimization for Constrained Optimization

    

    Introduction to Sequential Unconstrained Minimization for Constrained Optimization Tiedosto PDF

    brief history of SUMT & IP methods

    logarithmic barrier function

    central path

    basic SUMT

  • Valitse aktiviteetti Assignment 1

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Assignment 1 Tehtävä

    Convex Sets

    Due to October 8, 2023

  • Valitse aktiviteetti Assignment 2

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Assignment 2 Tehtävä

    Convex Functions

    Due to October 29, 2023.

  • Valitse aktiviteetti Solutions to Assignment 2

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Solutions to Assignment 2 Tiedosto PDF
  • Valitse aktiviteetti Assignment 3

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Assignment 3 Tehtävä

    Convex Problems

    Due to November 12, 2023.

  • Valitse aktiviteetti Assignment 4

    Saatavilla vasta, kun: You are a(n) Opiskelija

    

    Assignment 4 Tehtävä

    Duality, Applications, and Algorithms

    Last Assignment!

    Due to November 26, 2023.