Mathematical Optimization — Assignment 2 - IFOR

with a i = 0 satisfy c T x i ≤ 1 and all points with a i = 1 satisfy c T x i > 1. Formulate the decision
problem as a linear optimization problem.
(b) Given are m points (x i ,y i ), i = 1,...,m, such that x i ∈ IR n and y i ∈ IR. The aim is to find
vectors b 1 , b 2 , and c such that the hyperplane c T x = 1 partitions the m points into two parts and
the following expression is minimized:
∑ ∑
|y i −b T 1x i |+ |y i −b T 2x i |.
{i:c T x i≤1}
{i:c T x i>1}
Formulate a mixed-integer linear optimization problem to determine the vectors b 1 , b 2 , and c.
(Due date: Friday, March 9th, 2012, before the exercise class)
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