Consider the following optimisation problem: minimize fo (2) (1-2)+4(2-6) subject to f1 (2) = 1221 +...

   

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Consider the following optimisation problem: minimize fo (2) (1-2)²+4(2-6)² subject to f1 (2) = 1221 + 6(2+1)2 <16 *1=2 NO 22≥0 1. Visualise the problem (plot the functions on the 1-2 plane). Use the m-file Assgnmt 3.HELP available: on Canvas as a template. [0.5 point] 2. Find the optimal solution visually. Which constraints are binding? What can you say about the Lagrange multipliers associated with the constraints that are not binding? [0.5 point] 3. Solve the optimisation problem using the KKT conditions. Use the solution from the previous step as a guidance when eliminating candidate complementary slackness solutions! [1 point] 4. Solve the optimisation problem using Matlab's solver fmincon. Use the m-file Assgnmt 3.HELP available on Canvas as a template. [1 point] 5. Solve the optimisation problem using the barrier method. Use Matlab's function fmincon for the cen- tering step (inner iterations). See Slide 14 (Equation 6 describes the centering step) and Slide 22 (Al- gorithm I describes the barrier method) for guidance. Note that you only solve the centering step using Emincon! [1 point] 6. Solve the optimisation problem using the barrier method using the Newton's step for the inner iterations. Use Slide 20 describing the Newton step for guidance. [1 point] Hint: Use Matlab's Symbolic Math Toolbox to derive the expressions for the gradient and the Hes- sian of the barrier penalty term (V6(x) and V26(a) on Slide 20). Use the following parameter values: t=0.1 and 2. Use r =[0.2, 0.2] as the starting point. Consider the following optimisation problem: minimize fo (2) (1-2)²+4(2-6)² subject to f1 (2) = 1221 + 6(2+1)2 <16 *1=2 NO 22≥0 1. Visualise the problem (plot the functions on the 1-2 plane). Use the m-file Assgnmt 3.HELP available: on Canvas as a template. [0.5 point] 2. Find the optimal solution visually. Which constraints are binding? What can you say about the Lagrange multipliers associated with the constraints that are not binding? [0.5 point] 3. Solve the optimisation problem using the KKT conditions. Use the solution from the previous step as a guidance when eliminating candidate complementary slackness solutions! [1 point] 4. Solve the optimisation problem using Matlab's solver fmincon. Use the m-file Assgnmt 3.HELP available on Canvas as a template. [1 point] 5. Solve the optimisation problem using the barrier method. Use Matlab's function fmincon for the cen- tering step (inner iterations). See Slide 14 (Equation 6 describes the centering step) and Slide 22 (Al- gorithm I describes the barrier method) for guidance. Note that you only solve the centering step using Emincon! [1 point] 6. Solve the optimisation problem using the barrier method using the Newton's step for the inner iterations. Use Slide 20 describing the Newton step for guidance. [1 point] Hint: Use Matlab's Symbolic Math Toolbox to derive the expressions for the gradient and the Hes- sian of the barrier penalty term (V6(x) and V26(a) on Slide 20). Use the following parameter values: t=0.1 and 2. Use r =[0.2, 0.2] as the starting point.

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1 Visualize the Problem To plot the functions on the 2D plane you can define a range of xvalues calculate the corresponding yvalues using the given functions and plot the graphs You can use MATLABs pl... View the full answer