# Tagged Questions

Optimization is the process of choosing the "best" value among possible values. They are often formulated as questions on the minimization/maximization of functions, with or without constraints.

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### McCormick Envelopes with more then 2 variables

I'm trying to solve a bilinear optimization problem by linearizing the problem using the McCormick Envelope method. It's quite a simple method when you are only using the product of two variables, ...
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### Distance between a point and a conic curve

I have a point $r=(100,0)$ and want to find the closest point to it from this set: $$k = \{(a,b) : b^2=1+a/4\}$$ where $a$ belongs to $[-4,0]$. I thought about defining function $h(x)=|r-x|$, and ...
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### Optimization: maximum area of a triangle under a parabola

Optimization: maximum area of a triangle in a parabola Inside a curve ($x^2-25$ - Parabola) a triangle is drawn with A as the vertex at the origin and the line joining points B and C lie on the ...
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### Logistic regression for football results - Estimating coefficient through maximum likelihood

Consider two football teams $V$ and $L$ with strengths $W_V$ and $W_L$, respectively. Let's assume that the draw probability $\mathbb{P}(Draw)$ is known. Then this model is supposed to give estimates ...
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### Can't find minimum using Lagrange multipliers

I want to find the minimum of the function $f(x,y) = x + y^2$ with the constraint $2x^2 +y^2 = 1$. Here are my partial derivatives: $$f_x = 1$$ $$f_y = 2y$$ $$g_x = 4x$$ $$g_y = 2y$$ I have the ...
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### How write one optimization formula.

In this game I start with a Galleon with capacity 400. I can upgrade the harbor to get more Galleons, or upgrade the technolgy to increase the Galleon base cargo size by 10%. Right now have 8 ...
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### What are spurious local optima?

I keep seeing that word "spurious" (when used in the context of optimization), but I'm having trouble finding a good reference on what the definition of the term is.
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### floor/ceiling/round functions in the constraints of an optimization?

I have a constrained optimization problem in which I have to impose a "floor" or "ceiling" constraint to the solution. In fact I decided to use these nonlinear rounding functions because I needed to ...
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### What are some applications of vertex separators?

What are applications of finding a vertex separator that minimizes a cut in a graph. To clarify the problem I am talking about is is given a graph of n vertices and a partition $m_1,m_2,..,m_k$of ...
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### Robusness of median

If we let $X$ be a set of pints in $\mathrm{R}^2$, and let $g(X) = \arg \min_{y \in \mathrm{R}^2} \sum_{x_i \in X} \parallel x_i -y \parallel_2$ (geometric median of $X$). If $X$ and $X'$ are ...
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### How to calculate the hessian of a matrix function

I am estimating a model minimizing the following objective function, $M(\theta) = (Z'G(\theta))'W(Z'G(\theta))$ $Z$ is an $N \times L$ matrix of data, and $W$ is an $L\times L$ weight matrix, ...
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### Maximum und Minimum [closed]

I need help for c) also I solved a and b, but c) I could not. Let $f~:~\Bbb R^2\to \Bbb R$ be defined as $f(x,y)=e^{-x^2-y^2+2x-2y}$ a) Determine all local extrema for $f$. b) Determine all ...
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### Optimization of function on integer hypertetrahedron

I have the following optimization problem: Let $k,n \in \mathbb{N}$ with $k < n$. Let $N:=\{1, \dots,n\}$ and $D := \{^{t}(x_1, \dots, x_k) \in N^k \vert \sum_{i=1}^k x_i = N\}$ (hypertetrahedron)...
My textbook ask to find the extrema of $f(x,y) = 2x^2+y^2$ on $x^4-x^2+y^2-5=0$. It uses the lagrangian multipliers to find critic points.. Then it computes the function on these points then says "...