Show that || Ar +b|3 cTx +d f(x) = {x |c"x +d > 0}, where A E RmXn, bE Rm, c€ R" and d e R.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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please send handwritten solution for Q 3.23 part b Only Handwritten solution accepted
3.23 Perspective of a function.
(a) Show that for p > 1,
|x1|P + . ..+ |n|P
f (x, t) =
tp-1
tp-1
is convex on {(x, t) | t > 0}.
(b) Show that
|| Ax + b||3
cT x +d
f(x) =
is convex on {x | c" x + d > 0}, where A E Rmxn, b E R™, c E R" and d e R.
Transcribed Image Text:3.23 Perspective of a function. (a) Show that for p > 1, |x1|P + . ..+ |n|P f (x, t) = tp-1 tp-1 is convex on {(x, t) | t > 0}. (b) Show that || Ax + b||3 cT x +d f(x) = is convex on {x | c" x + d > 0}, where A E Rmxn, b E R™, c E R" and d e R.
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