Solutions Manual to Accompany Nonlinear Programming: Theory and Algorithms by Bazaraa Mokhtar S. Sherali Hanif D. Shetty C. M. & Hanif D. Sherali & C. M. Shetty
Author:Bazaraa, Mokhtar S., Sherali, Hanif D., Shetty, C. M. & Hanif D. Sherali & C. M. Shetty
Language: eng
Format: epub
Publisher: Wiley
Published: 2014-08-19T16:00:00+00:00
Therefore, b. The continuity of , where λ ≡ (λ1, λ2, λ3), follows directly from the definition of continuity and the fact that θ is continuous. Hence, we need to show that whenever θ1, θ2, and θ3 are not all equal to each other. The minimizer λ* of the quadratic fit function lies in the interval (λ1, λ3). Let θ* ≡ θ(λ*). First, suppose that λ* > λ2. If θ* ≥ θ2, then and θ* < θ3 (by the strict quasiconvexity of θ and since θ1, θ2, θ3 are not all equal to each other), and so If θ* < θ2, then and noting that θ* < θ1 since θ* < θ2 ≤ θ1, we get Hence, in this case. Similar derivations lead to if λ* < λ2, and likewise if λ* = λ2.
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