Topic outline

  • General

    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


    • Forum icon
      Announcements Forum
    • File icon
      Introduction and Overview File
      Pdf-tiedosto

      What the course is about

    • File icon
      Useful Concepts and Facts from Linear Algebra File
      Pdf-tiedosto

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

    • File icon
      Convex Sets File
      Pdf-tiedosto

      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

    • File icon
      Convex Functions File
      Pdf-tiedosto

      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

    • File icon
      Convex Optimization Problems File
      Pdf-tiedosto

      abstract form problem

      standard form problem

      convex optimization problem

      standard form with generalized inequalities

      mulitcriterion optimization

      restriction and relaxation

    • File icon
      Linear and Quadratic Problems, Semidefinite Programming (SDP) Format File
      Pdf-tiedosto

      linear programming (examples and applications)

      linear fractional programming 

      quadratic optimization problems 

      (quadratically constrained) quadratic programming 

      examples and applications 

      Semidefinite programming 

      applications

    • File icon
      CVX Tutorial File
      Pdf-tiedosto

      How to use solvers to solve convex optimization problems

    • File icon
      Duality File
      Pdf-tiedosto

      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

    • File icon
      Smooth Unconstrained Minimization Algorithms File
      Pdf-tiedosto

      terminology

      general descent method

      line search types

      gradient method

      steepest descent method

      Newton's method

    • File icon
      Introduction to Sequential Unconstrained Minimization for Constrained Optimization File
      Pdf-tiedosto

      brief history of SUMT & IP methods

      logarithmic barrier function

      central path

      basic SUMT

    • Assignment icon
      Assignment 1
      Not available unless: You are a(n) Student

      Convex Sets

      Due to October 8, 2023

    • Assignment icon
      Assignment 2
      Not available unless: You are a(n) Student

      Convex Functions

      Due to October 29, 2023.

    • File icon
      Solutions to Assignment 2 File
      Pdf-tiedosto
      Not available unless: You are a(n) Student
    • Assignment icon
      Assignment 3
      Not available unless: You are a(n) Student

      Convex Problems

      Due to November 12, 2023.

    • Assignment icon
      Assignment 4
      Not available unless: You are a(n) Student

      Duality, Applications, and Algorithms

      Last Assignment!

      Due to November 26, 2023.