# Questions tagged [approximation]

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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 $\mathbf{X}=\mathbf{x}^H\mathbf{x}$...
83 views

### 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 ...
239 views

### 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 ...
46 views

### 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 ...
1 vote
47 views

### 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 \...
89 views

### 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 $U$ ...
74 views

### 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 ...
60 views

### 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 ...