Questions tagged [approximation]

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What approximation is guarantees when solving an LP with floating-point numbers?

Given a linear program $$\begin{align} \text{maximize} \quad & c^{T}x \\ \text{s.t.} \quad & A x \leq b \end{align} $$ I can solve it exactly in polynomial time, using e.g. interior-point ...
Erel Segal-Halevi's user avatar
2 votes
1 answer
89 views

Approximating a convex program

As I understand it, "approximating" a convex program usually refers to finding a solution that is approximately-feasible approximately-optimal. For example, in the book "Geometric ...
eden hartman's user avatar
0 votes
1 answer
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Formulation of a stepwise linear approximation

I am currently trying to solve an MILP in Gurobi. Unfortunately, Gurobi does not support non-linear functions and I would like to do the following. I currently have the following constraint. It ...
nflgreaternba's user avatar
0 votes
1 answer
92 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 ...
Muhammad's user avatar
0 votes
1 answer
267 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 ...
Muhammad's user avatar
0 votes
2 answers
73 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 ...
Mostafa's user avatar
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1 vote
0 answers
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 \...
Ghulam Mohy-ud-din's user avatar
-1 votes
2 answers
92 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 $U$ ...
Ghulam Mohy-ud-din's user avatar
2 votes
1 answer
76 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 ...
user10837's user avatar
2 votes
1 answer
61 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 ...
Daniele Cuomo's user avatar
3 votes
0 answers
88 views

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,...
Jose_Peeterson's user avatar
1 vote
1 answer
166 views

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\...
Shayan zargari's user avatar
4 votes
1 answer
155 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: ...
Clement's user avatar
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