# Tagged Questions

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### Moment Generating Function of a Beta random variable.

After getting some excellent help on this problem in the statistics SE, I am reformuluating my question. Let me know if I should just delete it and ask a new one. Let $V$ be a $Beta(\alpha,1)$ ...
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### Shared groceries expenses between roommates to be divided as per specific consumption ratio and attendance

My apologies if this question is in the wrong section. Couple of my roommates & I (total 5 people) share the groceries expenses. We record the purchases in an Excel sheet, and also have the ratio ...
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### How to find a separating hyperplane?

I know about support vector machine, and it's quadratic programming approach which delivers the best separating hyperplane. My question is: is there a relatively simple algorithm to find a ...
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### Bounding volume of catmull-rom splines

I need to compute a 2D "spherical" bounding volume for the part of a catmull-rom spline $S(t)$ with four control points $P1$, $P2$, $P3$ and $P4$ in the domain $0 \le t \le1$. The purpose is to reduce ...
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### Newtons Method for approximation of absolute maximum [closed]

Use Newton's method (with $x_0 = 2.0$) to approximate the absolute maximum (correct to $5$ decimal points) of $f(x)=x\sin(x)$ on the interval $[0, \pi]$. Using Newton's method, the error does not ...
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### Definition of Global Convergence

I am confused by the notion of "global convergence" as used in numerical optimization literature, and did not find an exact definition for that yet. Now I try to double check my understanding here. ...
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### algorithm to find the root of a real-valued function $f$

I see in a book the following algorithm to find the root of a real-valued function $f$ $$\theta_{n+1} = \theta_{n} + \epsilon f(\theta_n); \epsilon >0$$ with the condition that the initial ...
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### Get number equation using specific set of values for get given answer

I have do it for AI assignment. Need a logic for finding solution ..Here is the explanation of problem . I have answer ( any number like for example 10 ). And have some set of numbers (like for ...
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### normal equations of $y(t) = \gamma e^{\lambda t}$ for minimizing the error

Let $y(t) = \gamma e^{\lambda t}$ and we have the points $(0,2)\ (1,0.7)\ (3, 0.3)$. The task is to get the parameter so that error is minimal. So we need to get the matrix for the normal ...
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### Hornâ€“Schunck method. Explanation of iterative solution

I am reading this paper (explanation of Horn-Shunck method for finding optical flow) and trying to understand it. My stumbling block is obtainig solution of system of linear equations I(x, y, t) ...
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### Reference for gradient descent with unit norm constraint

I faced a non-convex optimization problem with unit norm constraint. I can solve the problem using the gradient descent method and the projection of the gradient onto the tangent plane as in @joriki ...
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### Global optimization

Assume that I want to find the global minimum of a non-linear, non-convex, multidimensional function subject to several restrictions. Could you recommend me any deterministic strategy which can ...
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### Quadratic Optimization Problem with Box Constraints

I want to solve a problem of form $$\min_x x'Ax + b'x \;\;\mbox{ s.t. } l\leq x \leq u$$ where $A$ is a positive semidefinite matrix, thus the function I'm optimizing should be convex. However the ...
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### How to characterise this non-linear optimisation (linear objective function, non-linear constraints)

I was wondering if someone may be able to help me characterise this optimisation problem as I am struggling to find a numerical library that will solve it and I suspect it is because I am using the ...
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### Looking for a window containing the solution of an equation

I need to solve billions of times equations $\,f(x)=0\,$ with $$f(x) := \sum_{i=1}^N \frac {z_i}{c_i + x}$$ All $z_i$ are positive and add to $1$. Among the $N$ coefficients $c_i$, $M$ are negative ...
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### Optimizing trigonometric and nonlinear functions

First, Please, keep in mind that I'm a programmer not mathematician, and I have a fair mathematical background. I used optimization in Java to fit some observations to a trigonometric function, I ...
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### What numerical optimization method to use for this function?

In order to solve this over-determined system of equations numerically:  f_l(\mathbf x) = \displaystyle \left \lvert \sum_{k=1}^Kx_k^2e^{-j\frac{2\pi}Np_kl} \right \rvert , \qquad P = ...