Projective Transformations for Interior Point Methods
Projective Transformations for Interior Point Methods
Robert Michael Freund
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■ h->0 0->O h->0 We then prove the following three propositions, after which the proof of superlinear convergence easily follows. Proposition 5. 2. For any h > 0, at Step 6 of the algorithm, if y ky 2 (f(h))^ Proof: F(x NEW )-F( x) > k\l + y- V 1 + 2 Y / from (2. 4). Now substituting f(h) for 6 in Proposition 4. 1(c), we obtain the desired result. ■ Proposition 5. 3. Suppose h > and sufficiently small and f(h) and p(h) are defined as in Proposition 5. 1. At Step 6 of the algorithm, if y
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