# Tagged Questions

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### find of value Zx and Zy

I try to solve this Z^2+ZY+XY=0, and find the value of ZX and ZY, but couldn't find any hint in the web neither in a couple of calculus books for this particular equation. I have no clue about how to ...
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### Eliminate 2 variables from 3 equations with lots of parameters

I want to eliminate the variables x and y from these 3 equations in a way that all parameters appear in one equation without x and y: ...
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### Minimization problem with amplitude constraint

I have the following minimization problem: $$\left\| \bf{A}x - y\right\|^2 \to min$$ $$s.t. \left|x_i\right| < 1, \forall i,$$ where $\bf{A}$ is the complex matrix with size of $(n\times m)$, ...
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### How to solve Bellman's optimal equation from the first principle

How to solve the following set (finite) of equations $$v_*(s) = \max_{a\in A(s)} \sum_{s'} p(s'|s,a) [r(s,a,s') + \gamma v_*(s')]$$ $p$ and $r$ functions are given.
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### What is a minimal equation system?

In the optimization seminar I have to study the quadratic linear ordering problem. And there is one lemma saying some equations form a 'minimal equation system' of a polytope. Does anybody know, what ...
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### Strong duality in trace maximization

I'm working on understanding the derivation of the solution for principal components analysis. Let $\mathbf{S} \in \mathbb{R}^{p \times p}$ be a positive semi-definite matrix with rank $d < p$. ...
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### Nonlinear least squares and polygon area

I found this paper that describes preserving the global area of a polygon given some deformation (section 5): http://www.kunzhou.net/publications/2DShape.pdf I'm trying to do something very similar. ...
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### Linear Algebra Simplification Query

Apologies in advance; my linear algebra is not exactly up to scratch, but a program optimisation problem I've come across just feels like theres a better way mathematically rather than ...