# Tagged Questions

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### Minimizing a linear function on a strictly convex set.

All the theorems that I know considering the uniqueness of a solution to a minimization/maximization problem requires the strict convexity/strict concavity of the objective function. But consider the ...
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### Help in Linear summation of n(any given number)

The original formula is this. We're computing the complexity of an insertion sort. How did the first formula turned into the second formula?
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### Taylor's theorem for vector valued functions

I'm reading about linear and nonlinear programming and on one page I have the following statment (I have highlighted the areas where I have problems and drawn questions for them in the bottom of it): ...
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### Calculating second derivative of $g(\alpha) = f(\textbf{y}(\alpha))$

I'm having problems with the second derivative of the function $g(\alpha) = f(\textbf{y}(\alpha))$ (which I will define more precisely below). I tried calculating it myself, could anyone just simply ...
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### non linear equations solving methods?

I need to find $l_{2}$ and $\theta$ numerically by solving below equations. How could I do that? At least do i have some iterative way of finding those two unknowns. All others parameters are ...
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### A sufficient condition for a unique maximum of the product of two concave functions

Given two concave functions $f(x)$ and $g(x)$, what conditions in terms of these functions can ensure that $h(x)=f(x)g(x)$ have a unique maximizer on an interval $[a,b]$ for $a<b$?
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### Maximum of a product of a polynomial with positive coefficients and a finite sum of exponentials with negative coefficients on $[0,+\infty)$

Prove or disprove that $$f(x)=\left(\sum_i a_i x^i\right)\left(\sum_j b_j e^{-\lambda_j x}\right)$$ where $\forall i, a_i>0$, $\forall j, b_j>0,\lambda_j>0$, and both sums are finite, ...
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### Minimization of $\sum \frac{1}{n_k}\ln n_k >1$ subject to $\sum \frac{1}{n_k}\simeq 1$

Looking at an algorithm for minimizing $\sum_{k=1}^{m} \frac{1}{n_k}\ln n_k > 1$ subject to $\sum_{k=1}^{m}\frac{1}{n_k} = 1$ in which $n_k$ are positive and in general non-sequential integers, I ...
Using the implicit function theorem one can prove the following: Let $X,Y$ be Banach-spaces, $U\subset X$ open, $f\colon U\to \mathbf{R}$, $g\colon U\to Y$ continuously differentiable function. If ...
Motivation: Example. To solve a problem on evaluating the maximum of a product of $n$ real variables subject to an equality constraint on its sum $S$ ($=100$), I used the Lagrange multipliers method ...