# 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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### 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 helping me at ...
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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 ...
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### Maximize ratio of logarithms

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 ...
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### KKT conditions for non-convex almost everywhere differentiable problems

Consider the context of constrained function minimization. The well-known KKT conditions do not require the objective or constraint functions to be convex, but they do require them to be ...
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### Wolfram alpha error in global minimization?

Let us consider the function $$f(x,y)= x + y^2 - \ln(x+y)$$ If you try to minimize it using Wolfram Alpha (http://www.wolframalpha.com/input/?i=minimize+x%2By%5E2-ln%28x%2By%29), it founds a local ...
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### short-sale constraint with nonpositive-definite matrix in portfolio optimization

This question is about portfolio optimization in R. I have a nonpositive-definite matrix. I have handled with the singularity. Unfortunately, quadprog etc. optimization packages fail to solve the ...