Find the solutions of Lagrange multiplier = In the lecture of Online, Constraint, and Convex Optimization...

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Find the solutions of Lagrange multiplier = In the lecture of Online, Constraint, and Convex Optimization we learned how to find the minimum of the function under the constraint, using the Lagrange multiplier. Using the equations given in Slide #20, find the minimum of f(x,y) = x² + y², s. t. 2x + y ≤-4. Express the value of x, y, and fmin (x, y) and compare them with the corresponding values without constraints. min f(x, y)= x² + y² x, y s.t.2x+y≤-4 ▪ Lagrange multiplier L = x² + y² + 2(2x+y+4) ▪ Evaluate VL(x, 2,v) = 0 <> ᎧᏞ əx = 0, 200 180 160- 140 120- 100- 80- 60 40 20 0 -10 ƏL əλ --5 0,0L = 0 ὃν 10 -30 -20 -10 Find the solutions of Lagrange multiplier = In the lecture of Online, Constraint, and Convex Optimization we learned how to find the minimum of the function under the constraint, using the Lagrange multiplier. Using the equations given in Slide #20, find the minimum of f(x,y) = x² + y², s. t. 2x + y ≤-4. Express the value of x, y, and fmin (x, y) and compare them with the corresponding values without constraints. min f(x, y)= x² + y² x, y s.t.2x+y≤-4 ▪ Lagrange multiplier L = x² + y² + 2(2x+y+4) ▪ Evaluate VL(x, 2,v) = 0 <> ᎧᏞ əx = 0, 200 180 160- 140 120- 100- 80- 60 40 20 0 -10 ƏL əλ --5 0,0L = 0 ὃν 10 -30 -20 -10