Discussion
Which of the following is not true regarding the Karmarkar's algorithm ?
Answer: C
The statement that is not true is constraints are assumed to be non-homogeneous.
Karmarkar's projective algorithm works with a problem in a special canonical form: minimise \(c'x\) subject to homogeneous constraints \(Ax = 0\), \(\sum x_{j} = 1\), \(x \ge 0\). The centre of the simplex, \(x = (1/n, \ldots, 1/n)\), is assumed to satisfy \(Ax = 0\), and the algorithm starts from this interior point, moving through the interior rather than along the edges.
So (A) and (B) describe it, and, being a polynomial-time interior point method, it typically needs far fewer iterations on large problems (D). Non-homogeneous constraints are not part of its assumptions.
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