# 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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### Dual cone of a L1 norm cone?

I am listening to convex optimization lectures and I hear that dual cone of a $L1$ norm cone is a $L-\infty$ norm cone. Can anybody please explain how? I understand that every point in the dual cone ...
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### Extreme of $\cos(A)\cos(B)\cos(C)$ in a triangle without calculus.

If $A,B,C$ angles of a triangle, show extreme value of $$\cos(A)\cos(B)\cos(C)$$ I have tried using $A+B+C=\pi$, and applying all and any trig formulas, also AM-GM, but nothing helps. On this topic ...
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### Does it pay to know what you know?

Let's play a game. I ask you question a yes/no question, and you answer. You don't answer with a yes or no though, you answer with a probability of it being yes ($P \in (0,1)$). For example, I might ...
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### When might some a variable leave the basis?

In the simplex algorithm in linear programming, what are conditions for a variable to leave a basis (not necessarily basis for the/an optimal solution)? I'm supposed to list as many sufficient and ...
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### A primitive function of $e^{x^{2}}$

I made some efforts to set a closed form of primitive function of $e^{x^{2}}$ i find this function : $f(x)=\frac{x}{2x^{2}-1}e^{x^{2}}$ where : $f'(x)=(\frac{x}{2x^{2}-1}e^{x^{2}})'$= ...
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### Application of A.M. -G.M. inequality

Let x, y,z be positive numbers. The least value of $\frac{x(1+y)+y(1+z)+z(1+x)}{(xyz)^{.5}}$ is a) $\frac{9}{2^{.5}}$ b) 6 c) $\frac{1}{6^{.5}}$ d.) None of the above I tried applying the A.M. ...
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