# Tagged Questions

17 views

### Chain rule to compute the Jacobian of a geometric transformation

This question is related to image alignment. I'm transforming some points in homogeneous coordinates then "de-homogenouzing" them. The transformation is a rigid-body transform in 3D parameterized by ...
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### Hessian of a non-linear Matrix function

Apologies if this is a silly question, but I am really confused. I am trying to find the Hessian of a non-linear function $f$. I understand that the Hessian of $f$ with respect to $A$ is the Jacobian ...
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### Finding the maximum/minimum of a homogeneous function on $R^n$

Suppose that $f:R^n\to R$ is homogeneous. Also, suppose that the $argmin_xf(x)$ is non-empty. Is it true that if there exist $x^*\in R^n$ such that $f(x^*)=0$, then $x^*=argmin_xf(x)$?
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### An indirect optimizing problem

we have $z_1=x_1y_1$ , $z_2=x_2y_2$ and $z=xy$. we know $x<x_1+x_2$ and $y<y_1+y_2$. Can we conclude minimizing $z_1$ and $z_2$ will lead us to minimum (or lesser values) of $z$? ...
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### Homework: Proving stationary point over a closed convex set.

I'm stuck on this and need some help. I know the definition of a stationary point over a set. $x \in X \implies \nabla f(x^*)^T(x-x^*) >= 0$ How do i show it? I've thought of beginning by ...
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### Prove that a multivariable function doesn't have global extremes

So my question is actually this. Say I have a function $F:\mathbb R^2\to\mathbb R$. If I find all the potential local extremes by finding the roots of the partial derivatives and I find that only one ...
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### Does having a zero eigenvalue preclude a matrix from being indefinite?

If a $3\times3$ matrix has a positive eigenvalue, a negative eigenvalue, and a zero eigenvalue, is it then, by definition, indefinite? I think so, since the matrix has both a positive and a negative ...
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### How do I find out if a critical point of a function is a maximum or a minimum?

If I've found the critical point of a function defined in some constraint (perhaps using Lagrange multipliers and the like); how do I find out if it's a relative/global maximum/minimum of a function ...
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### Newton step for functions which takes matrix arguments

I want to minimize a function $f(X)$ which takes a matrix $X$ as an argument, i.e. $\min_X f(X)$. Using a descent method I start at step $k$ with feasible matrix $X^k$ and get to the next $X^{k+1}$ by ...
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### How to calculate the Hessian of the Lagrangian at x and lambda

I'm working on a project that needs to solve a constraint optimization function. Currently, I'm using Knitro solver and it needs to calculate the the hessian of the lagrangian at x and lambda. I don't ...
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### How to optimize a rational function

Just a calculus problem: As a function of $K \geq 1$, what is the minimum value of $f/a + f/b + f/c + f/d + f/e$ subject to the following constraints? \begin{cases} 1 \leq a \leq c \\ 1 \leq b ...
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### A naive approach for nonlinear optimization on several real variables and one natural variable. Give examples of (potential) failure

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 ...