Questions tagged [approximation]
The approximation tag has no usage guidance.
11
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Direct or indirect approximation of an expression
The expression $\sum_{n=1}^{N}\mathcal{Re}\left(x_{n}\right)$ can be directly or indirectly approximated into $trace(\mathbf{X})$ form ? $x_{n} \in \mathcal{C}$ and $\mathbf{X}=\mathbf{x}^H\mathbf{x}$...
- 65
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1
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83
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Convex approximation of an expression with fraction for CVX
I have the optimization problem
$$\underset{\mathbf{x} \in \Bbb C^N}{\max} \left| \frac{\mathbf{x}a-b}{\mathbf{x}c+b} \right|^2$$
where $a$, $b$ and $c$ are some scalars. I want to solve this ...
- 65
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1
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239
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Convex approximation of an expression
I am trying to transform an expression given by
$$ \operatorname{trace} \left( {\bf{X} } \right) + \left( \sum_{n=1}^N \mathcal{R}(x_n) \right) $$ into convex from where $\mathbf{x}$ is complex in ...
- 65
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46
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Deriving a lower bound for a two-stage stochastic problem
Assume an inventory stochastic optimization problem in the following form:
$$\min\limits_{x\in X} c^\top x + \mathbb{E}_{\mathbb{\xi}}[\mathcal{Q}(x, \xi)]$$
Demand is the uncertain parameter, and is ...
- 2,086
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47
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Smooth approximation of a five phase piecewise linear function
I am looking for a smooth (continuous differentiable) approximation of the following five-phased linear function:
$$
P(U, R, P_r) = \begin{cases}
R(U_{max} - U) + R(U_{up} - U_{max}) + P_r; & U \...
-1
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2
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89
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How to apply smooth approximation to non-linear complementarity constraints?
$P =$
$ x, if U \geq U^{max} $
$ y, if U^{up} < U < U^{max} $
$ z, if U^{down} < U < U^{up} $
$ \alpha, if U^{min} < U < U^{down} $
$ \beta, if U \leq U^{min} $
Where $P$, and $U$ ...
2
votes
1
answer
74
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Normal approximation of Poisson distribution
I am fairly new to statistics. I am working on a list of items in stochastic vehicle routing problem with Poisson distribution and I need to do a normal approximation. I read a paper with the ...
- 21
2
votes
1
answer
60
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Find the shortest path connecting some (s,t) - a greedy (?) criterion to a multi-commodity flow problem
At page 7 from these slides there is a Greedy algorithm I want to implement.
It says
let $P_i$ be the shortest path (if one exists) that [...]
connects some ($s_j$, $t_j$) pair that is not yet ...
- 561
3
votes
0
answers
86
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Function approximation of a complex objective function
I would like to approximate the following objective function using a simpler function that can use be defined in gurobi.
\begin{equation}
\min_{I_{i,v}} \ \sum^{N_v}_{v}\sum^{TT_v}_{i} \ C_{loss,...
- 349
1
vote
1
answer
162
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Find an upper bound for an objective function
My objective function is $\log_2(1+{x^2y^2})$ and I found two upper bounds for $x^2$ and $y^2$.
For example, assumed that we have the following upper bounds:
$x^2\leq\text{constant}_1^2$ and $y^2\leq\...
3
votes
1
answer
148
views
Smooth approximation of $\max(f_1(x),f_2(x),\cdots,f_n(x))$
In the GAMS documentation concerning non-smooth optimization I found the following statement:
A smooth approximation for $\max(f(x),g(y))$ is as in the following example code:
...
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