ELEC-E5422 - Convex optimization I D, 09.09.2020-23.10.2020

Topic outline

• Materials
  • Select activity Syllabus

    

    Syllabus File PDF

    Course Description and Main Organizational Issues

  • Select activity Introduction

    

    Introduction File PDF

    Introduction to the Course

  • Select activity Linear Algebra Basics (Mostly for Self-Reading)

    

    Linear Algebra Basics (Mostly for Self-Reading) File PDF

    Linear Algebra Basics (Mostly for Self-Reading)
    

  • Select activity Convex Sets

    

    Convex Sets File PDF

    Subspace, Affinene set, Convex set, Convex cone, Their simple examples and properties; Combination and Hulls; Ellipsoids, Polyhedra, Norm balls; Affine and projective transformations; Separating and supporting hyperplanes; Generalized inequalities
    

  • Select activity Convex Functions

    

    Convex Functions File PDF

    Convex functions, Epigraph; Simple examples and Elementary properties; More examples and More properties; Jensen's inequality; Quasiconvex and quasiconcave functions; Log-convex and log-concave functions; K-convexity
    

  • Select activity Convex Optimization Problems

    

    Convex Optimization Problems File PDF

    Abstract form problem; Standard form problem; Convex optimization problem; Standard form with generalized inequalities; Multi-criterion optimization; Restriction and relaxation
    

  • Select activity Linear and Quadratic Problems; SDP Format

    

    Linear and Quadratic Problems; SDP Format File PDF

    Linear programming (LP); Examples and applications; Linear fractional programming; Quadratic programming (QP); Quadratically constrained quadratic programming (QCQP); Examples and applications; Semidefinite programming (SDP); Applications
    

  • Select activity CVX Tutorial

    

    CVX Tutorial File PDF
  • Select activity Smooth Unconstrained Minimization Algorithms

    

    Smooth Unconstrained Minimization Algorithms File PDF

    Terminology; General descent method; Line search types; Gradient method; Steepest descent method; Newton's method
    

  • Select activity Introduction to Sequential Unconstrained Minimization for Constrained Optimization

    

    Introduction to Sequential Unconstrained Minimization for Constrained Optimization File PDF

    Brief history of SUMT & IP methods; Logarithmic barrier function; Central path; Basic SUMT
    

  • Select activity The Matrix Cookbook

    

    The Matrix Cookbook File PDF

    http://matrixcookbook.com