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3. Consider the problem min x x,yER s.t. (x – 1)? + (y – 1)? < 1 (x – 1)? + (y + 1)² <1 Draw the choice set to argue the solution to this problem is (1,0). Argue that the KKT condition does not hold at the optimum (1,0). Then, find the reason that the KKT condition does not hold at the optimum by discussing the constraint qualification condition.

3. Consider the problem min x x,yER s.t. (x – 1)? + (y – 1)? < 1 (x – 1)? + (y + 1)² <1 Draw the choice set to argue the solution to this problem is (1,0). Argue that the KKT condition does not hold at the optimum (1,0). Then, find the reason that the KKT condition does not hold at the optimum by discussing the constraint qualification condition.

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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3. Consider the problem min x x,yER s.t. (x – 1)? + (y – 1)? < 1 (x – 1)? + (y + 1)² <1 Draw the choice set to argue the solution to this problem is (1,0). Argue that the KKT condition does not hold at the optimum (1,0). Then, find the reason that the KKT condition does not hold at the optimum by discussing the constraint qualification condition.
Transcribed Image Text:3. Consider the problem min x x,yER s.t. (x – 1)? + (y – 1)? < 1 (x – 1)? + (y + 1)² <1 Draw the choice set to argue the solution to this problem is (1,0). Argue that the KKT condition does not hold at the optimum (1,0). Then, find the reason that the KKT condition does not hold at the optimum by discussing the constraint qualification condition.
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