# 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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### Max - min problem of a quotient of norms

For the $2\times2$ matrix $\begin{bmatrix}4&0\\-3&-5\end{bmatrix}$ Part 1 Find nonzero vectors $u$ and $w$ that maximize and minimize respectively the quotient $||Av|| / ||v||$. Part 2 ...
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Consider the following (non-convex) optimization problem on the real variables $\lambda_\ell^\pm$ with $\ell=1,\ldots,n$ \begin{align} \mbox{maximize}&\quad \lambda_{1}^+-\lambda_{1}^--2\sum_{\...
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### Does the terms 'LP primal' and 'LP dual' usually refer to any primal/dual, or just the optimal primal/dual pair

As the title says, I'm wondering whether the terms LP primal and LP dual usually refers to any primal/dual pair of an LP (feasible or not), or just the optimal primal/dual pair. The reason that I'm ...
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### Is $\text{Trace}(e^{XA+A^TX})$ a convex function of X?

Is $\text{Trace}(e^{XA+A^TX})$ a convex function of $X$? $X$ is diagonal and positive definite, $A$ is symmetric negative definite definite. And by the way, what is the best way to solve a problem of ...
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### Finding Extremas of $|x|$.

I'm trying to find the extrema of$\mod(x)$ but I'm not being able to do so. My attempt: $f(x, y) = |x|$ $f_{xx} = 0, f_{yy} = 0, f_{xy} = 0.$ So, $D(x, y) = 0$. And second derivative test isn't ...
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### Maximum of $f(x) = (45-2x)\cdot (24-2x)\cdot (2x)\;,$ Where $0<x < 12$

How Can I Maximise $f(x) = (45-2x)\cdot (24-2x)\cdot (2x)\;,$ Where $0<x < 12$ Using Inequality $\bf{My\; Try::}$ In $0<x<12\;,$ The value of $(45-2x)\;,(24-2x)\;,2x>0$ and we can ...
How can one maximize the ratio of two logarithms $\frac{\log{f(x)}}{\log{g(x)}}$ where the argument to each logarithm is the (positive) ratio of two first-degree polynomials? I have tried ...
I'm working on a linear time varying discrete(LTV) multi input multi output(mimo) system. I formulate the problem description in the following way x_i(k+1) = x_i(k)\cdot A_i(k) + B_i(k)\cdot u_i(k)\$...