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3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only if A >o. Find the strang convetiky constont shen it strongly conrex.

3 Show thot tfe fundion fae Ax +26T* +C with A = AT E IR E IR", CE IR is strongly Convex if and only if A >o. Find the strang convetiky constont shen it strongly conrex.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Show thot the function fwe x'Ax +zbTx +C with A = AT E IR 6'E IR", ċE IR is strongly convex if andd only if A >o. Find the strong convexity constont shen it is strongly Convetity constont ishen it conrex. 3) Let : IR" IR be (onvedt ond AE IR mn. Denote h os min ahore it is ossumed Hhat hcy) >_ ∞ for dh y. Shou that h is con vet.
Transcribed Image Text:Show thot the function fwe x'Ax +zbTx +C with A = AT E IR 6'E IR", ċE IR is strongly convex if andd only if A >o. Find the strong convexity constont shen it is strongly Convetity constont ishen it conrex. 3) Let : IR" IR be (onvedt ond AE IR mn. Denote h os min ahore it is ossumed Hhat hcy) >_ ∞ for dh y. Shou that h is con vet.
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