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Consider the problem min (x³ + y³ + z³) s.t. x² +y? + z? = 1 (1) Is the feasible region of the problem convex? (2) Show that a point (x, y, z) is a KKT point of the problem if and only if x² +y² + z² = 1 and there exists 1 ER satisfying x = 22x, y² = 2^y,and z² = 2^z. %3D %3D

Consider the problem min (x³ + y³ + z³) s.t. x² +y? + z? = 1 (1) Is the feasible region of the problem convex? (2) Show that a point (x, y, z) is a KKT point of the problem if and only if x² +y² + z² = 1 and there exists 1 ER satisfying x = 22x, y² = 2^y,and z² = 2^z. %3D %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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Consider the problem min (x + y³ + z³) s.t. x² + y? + z² = 1 (1) Is the feasible region of the problem convex? (2) Show that a point (x, y, z) is a KKT point of the problem if and only if x +y² + z² = 1 and there exists 1 ER satisfying x = 2hx, y² = 2hy,and z² = 2\z.
Transcribed Image Text:Consider the problem min (x + y³ + z³) s.t. x² + y? + z² = 1 (1) Is the feasible region of the problem convex? (2) Show that a point (x, y, z) is a KKT point of the problem if and only if x +y² + z² = 1 and there exists 1 ER satisfying x = 2hx, y² = 2hy,and z² = 2\z.
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