0
votes
0answers
31 views

How to take partial derivative of summation?

This is about L$^1$ iteratively reweighted least squares. Where did the (-a$_i$$_k$) come from?
0
votes
1answer
19 views

Finding matching weight for two differing types of cat food

Attempting to figure out how much cat food to give my cat I came across a problem which I am unsure of any way other than iteration to solve. The problem I have is that I have been advised to feed my ...
1
vote
1answer
22 views

Gradient Question-Linear Regression

When discussing linear regression, we discuss the error of the out of sample data prediction. That is, $$ E_{\operatorname{out}} = \frac{1}{N} \sum_{n=1}^{N} ...
1
vote
1answer
75 views

First-order necessary condition for relative minimum point

I'm studying linear and nonlinear programming and I came across with the following proposition : given $\rm x\in\Omega$ we are motivated to say that a vector $\mathbf d$ is a feasible direction at ...
1
vote
1answer
343 views

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): ...
0
votes
1answer
34 views

Help with a property of a convex function

I'm studying linear and nonlinear programming and on my book I bumped into the following statement: $$\lim_{\alpha \to 0} \displaystyle \frac{f(\textbf{x}+\alpha ...
1
vote
0answers
32 views

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 ...
0
votes
1answer
44 views

Conditions for a system to be solvable.

I have the following system of equations: $$\begin{aligned} \left\{\begin{array}{l} a+dz+cy+exy = 0\\ 10a+3bx-exy =0\\ -5a-dz = 0 \end{array}\right. \end{aligned}~~.$$ I would like to solve for ...
4
votes
0answers
484 views

Maximum and minimum of an integral under integral constraints.

Find the maximum and minimum of the following integral in terms of $f(x),a,C$: \begin{align}I=\int_{0}^{a} \frac{x}{f(x)}p(x)dx \end{align} s.t.: 1) $\int_{0}^{a} p(x)dx=1$ 2) $\int_{0}^{a} ...
0
votes
2answers
107 views

Find $n$ in $8n^2 \le 64n\lg n$

Given the solution. Can someone help me why $n \le 43$. What is the step by step of the solution for this?
0
votes
2answers
265 views

Convex function from Hessian

Am I correct to say that the following function is convex? $$\begin{align} & f(x,y)=-\sqrt{xy} \\ & x>0,y>0 \\ \end{align}$$ After computing the Hessian: $$ Hf =\left[ \begin ...
2
votes
1answer
118 views

Critical Points. Find and classify.

Given $g(x,y)=y^2 - x^3$ find the critical points and classify them $$\nabla g(x,y) = \begin{pmatrix} -3x^2 \\ 2y \\ \end{pmatrix}$$ So, $\implies -3x^2=0,2y=0$ ...
2
votes
1answer
165 views

Lagrange multipliers for discrete variables

Is there a way to adapt the method of Lagrange multipliers to problems involving discrete variables? Unfortunately I don't have a specific problem to ask here (I haven't completely formulated it ...