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You wish to optimize a function f(x1,x2, X3) subject to two constraints g(x1, 2, x3) = 0 and h(x1,x2, x3) = 0. You have found one critical point which yields the bordered Hessian of the Lagrangian to be %3D

You wish to optimize a function f(x1,x2, X3) subject to two constraints g(x1, 2, x3) = 0 and h(x1,x2, x3) = 0. You have found one critical point which yields the bordered Hessian of the Lagrangian to be %3D

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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You wish to optimize a function f(x1, x2, X3) subject to two constraints g(x1, x2, 23) = 0 and h(x1, x2, x3) = 0. You have found one critical point which yields the bordered Hessian of the Lagrangian to be 1 2 -3 -1 -1 H = 1 -1 2 0 0 -3 -1 Select the value of the appropriate minor and classify the critical point. Select 2 correct answer(s) | Need |H3|.|H4| AND |H5| and we compute H3 = 0, |H4= 4, |H5| = 48 | Need |H3|.|H4| AND |H5|and we compute |Нз — 0, На— — 4, Нs| — - 48 O Need ONLY |H5| and we compute |H5|=48 %3| | Need ONLY |H5| and we compute|H5|= -48 Lagrange SOC tell us it is a local maximum | Lagrange SOC tell us it is a local minimum | Lagrange SOC tell us it is a saddle type point
Transcribed Image Text:You wish to optimize a function f(x1, x2, X3) subject to two constraints g(x1, x2, 23) = 0 and h(x1, x2, x3) = 0. You have found one critical point which yields the bordered Hessian of the Lagrangian to be 1 2 -3 -1 -1 H = 1 -1 2 0 0 -3 -1 Select the value of the appropriate minor and classify the critical point. Select 2 correct answer(s) | Need |H3|.|H4| AND |H5| and we compute H3 = 0, |H4= 4, |H5| = 48 | Need |H3|.|H4| AND |H5|and we compute |Нз — 0, На— — 4, Нs| — - 48 O Need ONLY |H5| and we compute |H5|=48 %3| | Need ONLY |H5| and we compute|H5|= -48 Lagrange SOC tell us it is a local maximum | Lagrange SOC tell us it is a local minimum | Lagrange SOC tell us it is a saddle type point
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