1
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1answer
28 views

Quadratic Problen with 2 constraints

Could someone help me to solve the following: $\min x^Tx$ s.t. $x^T a=1$ $x^T b=0$ where $x$,$a$ and $b$ are $(N\times1)$ vectors and $1$ and $0$ scalars. Thank you!
0
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0answers
17 views

Threshold in a maximisation problem (with KKT conditions)

I'm looking to maximise with respect to $x_i$ $$L = \sum_{i= 1}^n y_i \frac {x_i^{1 - \epsilon}}{1 - \epsilon}$$ subject to $ \sum_{i= 1}^n x_i = B $ and $x_i \ge 0$ for all $i$, where $y_i$, $B$ ...
0
votes
0answers
43 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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votes
0answers
10 views

$\text{min}_{\{n_j\}_{j=1}^{J}} \sum_{j=1}^J n_j c_j$, subject to $\sum_{j=1}^J n_j(j-p)=0$, $n_j\geq 0 \quad \forall j$

So I'm apparently very rusty on this sort of thing... $\text{min}_{\{n_j\}_{j=1}^{J}} \sum_{j=1}^J n_j c_j$ subject to $\sum_{j=1}^J n_j(j-p)=0$ $n_j\geq 0 \quad \forall j$ Then my Lagrangian is ...
2
votes
1answer
144 views

Optimization Problem: Karush-Kuhn-Tucker Condition

I am working on the question displayed below. I know that the method of Lagrange Multipliers is used to find the solution for optimization problems constrained to one or more equalities and when our ...
1
vote
2answers
103 views

Determine the points where $f$ is has a local minimum/maximum. Multivariable calculus question.

This is not homework, but it is in my book and I find it hard to solve: Determine the points where $f$ is has a local minimum/maximum. Determine if it strong/weak and absolute/relative and ...
1
vote
0answers
62 views

KKT: Explain visually the optimality condition $F_0\cap G_0\cap H_0=\emptyset$

I am trying to understand visually what this condition actually mean. It is the optimality condition in KKT. It means something like that constraint -set, objective -set and hyperplane -set has no ...
1
vote
1answer
748 views

Linear least squares with non-negativity constraint

I am interested in the linear least squares problem: $$\min_x \|Ax-b\|^2$$ Without constraint, the problem can be directly solved. With an additional linear equality constraint, the problem can be ...
1
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2answers
206 views

How can I infer a result using primal feasibility, dual feasibility, and complementary slackness?

I am trying to find the minimum of $-x_1$ with restrictions $\bar g\leq\bar 0$ so that $$\bar g=\begin{pmatrix} (x_1+2)^2+(x_2-4)^2-20\\ (x_1+2)^2+x_2^2-20\\ -x_1\end{pmatrix}\leq ...