Tagged Questions

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Finding extremal of a fixed end point problem. Optimisation

I want to find the extremal of the fix-end point problem $\int_1^2 \frac{\dot{x}^2}{t^3}$ with $x(1)=2,x(2)=17$ First I check the euler-lagrange equation is equal to $0$. We have: ...
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Maximize arccos-function

I need to find a maximum of the function $$y=\arccos\left(\frac{29+12x\sin(22)+6x\cos(22)+x^2} {\sqrt{x^2+6x\cos(22)-20x\sin(22)+109}\sqrt{x^2+6x\cos(22)-4x\sin(22)+13)}} \right)$$ between x=0 and ...
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Fractional part optimization algorithm

I was trying, out of curiosity, to find an efficient algorithm for the problem below which peaked my interest: Let $r$ be a real number. Find an integer $k > 0$ such that $kr$ is "near" an ...
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Notation for near optimal solution

Usually, $x^*$ is used to denote the optimal solution to a maximization problem. I need a notation to describe a solution that is not optimal but "good enough." In my case this solution is the first ...
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Local minimum global

Let $f:(a,b)\to\Bbb R$ be continuous. Assume that $f$ has a local minimum at some point $x_0$. Further assume that this is the only point where $f$ has a local extremum. Does it follow that $f$ has a ...
If a $3\times3$ matrix has a positive eigenvalue, a negative eigenvalue, and a zero eigenvalue, is it then, by definition, indefinite? I think so, since the matrix has both a positive and a negative ...