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1answer
23 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!
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15 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 $y_i$, $B$ ...
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0answers
38 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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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 ...
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1answer
135 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 ...
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1answer
40 views

Kuhn-Tucker conditions: why does $\lambda$ $\dfrac{\partial L}{\partial \lambda}=0$?

Satifying Kuhn-Tucker conditions. Given $\lambda$ is a row, and $\dfrac{\partial L}{\partial \lambda}$ is a column, why does $\lambda$ $\dfrac{\partial L}{\partial \lambda}=0$ ?
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1answer
29 views

Non linear programming please HELP

Hey guys, I never do that but just found out that I have an assignment due in a few hours..thought it was for later, any help/solutions for this one?
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2answers
1k views

Simple explanation of lagrange multipliers with multiple constraints

I'm studying support vector machines and in the process I've bumped into lagrange multipliers with multiple constraints and Karush–Kuhn–Tucker conditions. I've been trying to study the subject, but ...
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2answers
102 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 ...
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1answer
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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1answer
160 views

Check Kuhn-Tucker conditions

How to check if $(0,1)$ point is the solution of this optimization problem using Kuhn-Tucker Theorem. Find the min of $e^{x_1-x_2}-x_1-x_2$ where $x_1+x_2\le1,\ x_1\ge 0,\ x_2\ge0$ I am thinking ...
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0answers
60 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 ...
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1answer
724 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 ...
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2answers
202 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 ...
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2answers
157 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 ...