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May
31
comment Quantization minimizing the quadratic error
Yes ${y_1,y_2,\dots,y_N}$ and $f$ are optimization variables. Futhermore $f$ can't be injective (one to one) since $M > N$
May
30
comment Quantization minimizing the quadratic error
$f$ is simply a function from $\{0,\dots, M\}$ into $\{0,\dots, N\}$. It is a parameter of the minimisation.
May
28
awarded  Commentator
May
28
comment Can this multidimensional non-linear equation with constraints be minimized analytically?
First of all, as a software developper I am not a linear programmer expert. You should have noticed that this is a linearly constrained least-squares problem. And since you are constricting $w$ within a polyhedron. If the solution of the unconstrained least-squares problem lies within this polyhedron you're good. But in any other case, the solution will be on a face of the polyhedron. Which one ? It is a discrete non-continuous function of $P$ and $q$ which would invole many cases.
May
28
asked Quantization minimizing the quadratic error
Jan
25
comment Cyclic monotonicity of sub-differential domain and convex property
Thank you ! I will try to find this book next week. (I am sure it must exist an elegant proof to this characterization)
Jan
21
comment Did i formulate this Linear Optimization Problem right?
Yes I meant that way.
Jan
21
comment Did i formulate this Linear Optimization Problem right?
Why do you impose $x_1$ and $x_2$ to be positive ? Your constraint isn't linear. You need to split it into two linear constraints.
Jan
18
revised Cyclic monotonicity of sub-differential domain and convex property
edited title
Jan
18
revised Cyclic monotonicity of sub-differential domain and convex property
deleted 2 characters in body
Jan
18
awarded  Promoter
Jan
13
comment Cyclic monotonicity of sub-differential domain and convex property
ps : I am a french computer science student and I didn't have much time to delve deeper that's why I asked this question.
Jan
13
asked Cyclic monotonicity of sub-differential domain and convex property
Jul
1
awarded  Student
Jun
30
asked Vertex Definition (Linear optimization)
Dec
4
revised Prove $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$
added 46 characters in body
Dec
4
comment Prove $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$
Ok, thank you. :)
Dec
4
comment Prove $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$
@Thomas Andrew : Absolutely, thanks. ( I'm new on this kind of forum but is it recommended to edit my answer ?)
Dec
4
comment Prove $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$
I don't see what you are looking for, this is a proof,isn't it ? (I'm sorry I'm french and my english is ugly :()
Dec
4
answered Prove $\left|\frac{x^2y^3}{x^4+y^4}\right|\leq |x|+|y|$