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3. Consider the following quadratic programming problem: min -2x, – 2x2 + xỉ + 2x – 2x,x2 s.t. X1 +x2 < 3 2x1 + 3x2 2 6 X1,X2 2 0 a) Write down the KKT conditions. b) Suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem (with artificial variables added if necessary) that is to be addressed explicitly. Identify the additional complementarity constraint that are enforced automatically by the algorithm.

3. Consider the following quadratic programming problem: min -2x, – 2x2 + xỉ + 2x – 2x,x2 s.t. X1 +x2 < 3 2x1 + 3x2 2 6 X1,X2 2 0 a) Write down the KKT conditions. b) Suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem (with artificial variables added if necessary) that is to be addressed explicitly. Identify the additional complementarity constraint that are enforced automatically by the algorithm.

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 following quadratic programming problem: min -2x1 – 2x, + xỉ + 2x3 – 2x,x2 s.t. X1 +x2 < 3 2x1 + 3x2 2 6 X1, X2 2 0 a) Write down the KKT conditions. b) Suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem (with artificial variables added if necessary) that is to be addressed explicitly. Identify the additional complementarity constraint that are enforced automatically by the algorithm. c) Perform a single iteration of the modified simplex method to the problem formulated in part (b). Write down the entering and leaving variables clearly.
Transcribed Image Text:3. Consider the following quadratic programming problem: min -2x1 – 2x, + xỉ + 2x3 – 2x,x2 s.t. X1 +x2 < 3 2x1 + 3x2 2 6 X1, X2 2 0 a) Write down the KKT conditions. b) Suppose that this problem is to be solved by the modified simplex method. Formulate the linear programming problem (with artificial variables added if necessary) that is to be addressed explicitly. Identify the additional complementarity constraint that are enforced automatically by the algorithm. c) Perform a single iteration of the modified simplex method to the problem formulated in part (b). Write down the entering and leaving variables clearly.
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