By setting the gradient to 0, find the solutions to the following optimization problems: . Q1.1 argmin.J(x), where.J(x) = x² -2x+3 I Q1.2, y = argminJ(x, y), where J(x, y) = 2x² + 3y² - 4x + 12y +15 x.y Q1.3, y= argmin.J(x, y), where J(x, y) = x² + 4y² - 4xy+2x-4y+4 x,y Prove that J(x, y) in Q1.2 above is convex.
By setting the gradient to 0, find the solutions to the following optimization problems: . Q1.1 argmin.J(x), where.J(x) = x² -2x+3 I Q1.2, y = argminJ(x, y), where J(x, y) = 2x² + 3y² - 4x + 12y +15 x.y Q1.3, y= argmin.J(x, y), where J(x, y) = x² + 4y² - 4xy+2x-4y+4 x,y Prove that J(x, y) in Q1.2 above is convex.
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Transcribed Image Text:By setting the gradient to 0, find the solutions to the following optimization problems:
.
Q1.1 argmin.J(x), where.J(x) = x² -2x+3
I
Q1.2, y = argminJ(x, y), where J(x, y) = 2x² + 3y² - 4x + 12y +15
x.y
Q1.3, y= argmin.J(x, y), where J(x, y) = x² + 4y² - 4xy+2x-4y+4
x,y
Transcribed Image Text:Prove that J(x, y) in Q1.2 above is convex.
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