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42 views

KKT Conditions and Convexity

min $x^2 -xy +y^2 -5x+6y$ subject to $1 \leq y$, $y^3 \leq 2x$, and $x \leq 8$ Write out the KKT conditions for this problem. Show that $(x,y) = (4,2)$ is a KKT point, and is therefore a global ...
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54 views

KKT formulation

How to reformulate the following problem $$min \frac{1}{2} (x_1-a_1)^2+ \frac{1}{2} (x_2-a_2)^2$$ $$s.t. \mathbf{1}^Tx=1$$ $$ ||x||_2\leq2$$ as the following system of KKT conditions: $$(1 + ...
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163 views

What does the statement “Optimality condition for convex problem” mean? KKT or other condition?

I am stuck to the problem 4 here, course Mat-2.3139, the due day was yesterday. The hint is "Optimality-condition for a convex-problem". I have asked this now from 3 assistants and everyone with ...