../

CVXOPT Quiz 2

$\newcommand{\qq}{\quad\quad}$

Date

  • 10/20

Portions

Topic List

  • Definition of a convex problem
  • Transformations
    • Change of variables
    • Transform objective and or constraints
    • Eliminating affine equality constraints
    • Optimizing out some of the variables
  • Key facts about convex optimization problems
    • Local optimum is the global optimum
      • This isn’t based on differentiation
      • $f(x) \le f(x')\qq \forall x' \in B_{x, r}, r> 0$
    • $\nabla f_0 (x) = 0 \implies x$ is the global minimum
    • If $x^*$ is an optimum, then $\forall y\text{ (feasible) , } \nabla f_0(x^*)^T (y - x)\ge 0$
      • This is essentially what the Lagrange multipliers tell us
      • $\nabla f_0(x^*)$ is then a separating hyperplane
  • Linear Programming
  • Quadratic Programming

Book Chapters

Ch. 4 from B&V

Lectures

Practice Problems

PSET1

  • 4.8 (b)
  • 4.21 (b)

PSET2

 4.8 (a,c-f)

PSET3

4.21 (a,c)