Numerische Verfahren der restringierten Optimierung

Universität Konstanz Wintersemester 16/17 Fachbereich Mathematik und Statistik

Prof. Dr. Stefan Volkwein Jianjie Lu, Sabrina Rogg

Numerische Verfahren der restringierten Optimierung

http://www.math.uni-konstanz.de/numerik/personen/volkwein/teaching/

Sheet 2

Deadline for hand-in: 29.11.2016 at lecture

Exercise 4 (2 Points)

Consider the following linear program in R²:

minx₁ subject to x₁+x₂ = 1, (x₁, x₂)≥0.

Show that the primal-dual solution (solution to system (2.4) in the script) is x^∗ =

0

1

, λ^∗ = 0, µ^∗ =

1

0

.

Exercise 5

Given the problem

min (x−2)²+ 2(y−1)² subject to x+ 4y≤3, x≥y.

Set up the Lagrange function and solve the problem using the KKT system.