# 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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### What is the easiest way to optimize the weighted sum of L2 norms?

I have the following cost function (solving for $M$ - the $x_i$s are known): minimize $\sum_i\sum_j(w_{ij} \cdot (x_i-x_j)^T\cdot M\cdot(x_i-x_j))$ ($w_{ij} \in [-1,1]$) subject to: $M \succeq 0$ (...
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### Proof: $\underset{\|q\|=1}{\max} q^TAq = \lambda_{\max}$ with $q$ the corresponding eigenvector ($A$ symmetric)

This problem is quite old and there should be similar problems. I know the following technique: \begin{aligned} q^TAq=q^TU\Lambda U^Tq=(U^Tq)^T\Lambda (U^Tq) \end{aligned} \...
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### Absolute extrema

Find the absolute extrema of the function $f(x,y)=2xy-x-y$ over the region of the xy-plane bounded by the parabola $y=x^2$ and the line $y=4$ I was wondering if I needed to use Lagrange multipliers to ...
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### Binary Stochastic Programming with Independent or Positively Correlated Co-efficients

A manufacturer can select a maximum of $N$ stores to fulfill orders from a total of $M$ stores who are looking for inventory, $N\le M$. The case when $N\geq M$ is trivially solved when all stores ...
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### how to project optimal parameters on to feasible region

Hi: I'm trying to understand the concept of projection and I created a toy example that might help me to do that. Suppose that I have a non-linear optimization with 3 parameters theta_1, theta_2 and ...
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### Finding the nonnegative integer exponents that minimize a product

I've been trying to solve a problem which seems to be a multiplicative optimization problem: Given a threshold $T > 0$, and a set of integers $b_1, b_2,\dots, b_n > 0$, find integer ...
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### Calculus 1 - Optimization of a Box

Can you guys help me out with it? i try to solve it but my answer is so weird that i think im wrong... Question- Someone want to build cardboard box with rectangular base. Knowing thatthe rectangle ...
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### Extreme of $\cos A\cos B\cos C$ in a triangle without calculus.

If $A,B,C$ are angles of a triangle, find the 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 ...
Let $X$ be a banach space or simply a normed space and $C$ a convex (closed) subset of $X$. It is true that if $x \in C$ is such that $f(x)=\sup f(C)$, (in other words $x$ is a supporting point for $C$...