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# Lab 4 - ‐ linearity when you enter in the model however...

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University of Toronto Department of Mechanical and Industrial Engineering MIE376: Mathematical Programming Winter 2011 Lab 4 – Non Linear Programming and Quadratic Programming Gurobi 4.0 has the capability to solve quadratic programs. 1. Writing the Quadratic Program For the formulation: min 0.2ݔ ൅ 0.08ݔ ൅ 0.18ݔ ൅ 0.1ݔ ݔ ൅ 0.04ݔ ݔ ൅ 0.06ݔ ݔ subject to: 0.14ݔ ൅ 0.11ݔ ൅ 0.1ݔ ൒ 120 ݔ ൅ ݔ ൅ ݔ ൑ 1000 ݔ , ݔ , ݔ ൒ 0 In AMPL: Load the model into AMPL and solve. Only Gurobi 4.0 can solve the QP problems. Note : AMPL will accept any non
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Unformatted text preview: ‐ linearity when you enter in the model, however, the solver, Gurobi 4.0 will only solve the QP for quadratic objective functions, and will not solve for quadratic constraints. 2. KKT Conditions: Solve Problem 6 in Chapter 11.9 of the textbook: Confirm with the AMPL solution and find the λ ’s and μ ’s. var x1 >= 0; var x2 >= 0; var x3 >= 0; minimize ObjFunc: 0.2*x1^2 + 0.08*x2^2 + 0.18*x3^2 + 0.1*x1*x2 + 0.04*x1*x3 + 0.06*x2*x3; subject to Const1: 0.14*x1 + 0.11*x2 + 0.1*x3 >= 120; subject to Const2: x1 + x2 + x3 <= 1000;...
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• Spring '11
• Daniel
• Gurobi, quadratic objective functions, Industrial Engineering  MIE376, Mathematical Programming  Winter, University of Toronto  Department of Mechanical and Industrial Engineering, QP problems.      Note

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