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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section: Chapter Questions

Problem 4PT

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Question

Consider the constrained optimization problem
min (x²+(y)²)
x,y
subject to
x²+4y² = 4
X ≥ 0.
(a) Find all KKT points of this problem.
(b) Verify the linear independence constraint qualification (LICQ) at all KKT points you have
found in (a).
(c) Using second-order optimality conditions theorems, decide which of the KKT points are solu-
tions.
(d) Sketch a plot of the problem and its solution(s).

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