Problem 3. (30%) Answer the following questions on constrained optimization problems: (a) (15%) Consider the optimizatio

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Problem 3 30 Answer The Following Questions On Constrained Optimization Problems A 15 Consider The Optimizatio 1 (45.85 KiB) Viewed 14 times

Problem 3. (30%) Answer the following questions on constrained optimization problems: (a) (15%) Consider the optimization problem 1 min 11,72 (1₁ + 2)² + 1/(x₂-6) ² s.t. ₁+2x₂ = 2. Write down the KKT conditions (or the optimality condition via the Lagrange multipliers technique) for the equality constrained problem. You may let A be the Lagrange multiplier. Find a KKT point (1,, A*) to the problem. (b) (15%) Consider the optimization problem 1 min F1,F2 (1-3)²+(₂+1)² s.t. 271 +1₂ ≥0, z²+z²≤1. Write down the KKT conditions for the above problem. You may let 1 & 2 be the slack variables. corresponding to the first & second inequality, respectively. Find a KKT point (1, 2, 1, ₂) to the problem.