<p>Your question may be answered in the following paper:</p>

<p>@article{strang1983maximal,
  title={Maximal flow through a domain},
  author={Strang, G.},
  journal={Mathematical Programming},
  volume={26},
  number={2},
  pages={123--143},
  year={1983},
  publisher={Springer}
}</p>

CC BY-SA 3.0
2011-06-08T06:14:42.330Z
The paper does not take the approach that i want to follow. I believe that the dual can be obtained by simply finding the lagrangian function. I just did not know how to find the lagrangian dual function for the given function. I have now worked it out.
AnkurVj
CC BY-SA 3.0
2011-06-07T19:22:18.717Z
2011-06-07T19:22:18.717Z
Steven Gortler
<p>The continuous max flow problem is posed as follows : </p>

<p>sup $\int_\Omega  p_s(x)dx$</p>

<p>subject to : </p>

<p>$|p(x)| \le C(x);  \forall x \in \Omega $</p>

<p>$p_s(x) \le C_s(x);  \forall x \in \Omega $</p>

<p>$p_t(x) \le C_t(x);  \forall x \in \Omega $</p>

<p>$\nabla \cdot p(x) - p_s(x) + p_t(x) = 0;  \forall x \in \Omega $</p>

<p>Here $p(x)$ is a field vector and is analogous to the flow in the discrete domain. $\nabla \cdot p$ is the divergence of the field p.</p>

<p>How do i find out the dual of this maximization problem using the lagrangian dual technique, i.e. the equivalent min cut formulation of the problem in the continuous domain.</p>

<ds.algorithms><max-flow-min-cut><primal-dual>
Primal Dual model in the continuous domain
AnkurVj
# Primal Dual model in the continuous domain

(Asked by: username_0 on 2011-06-03)

The continuous max flow problem is posed as follows :

sup $\int\_\Omega p\_s(x)dx$

subject to :

$|p(x)| \le C(x); \forall x \in \Omega $

$p\_s(x) \le C\_s(x); \forall x \in \Omega $

$p\_t(x) \le C\_t(x); \forall x \in \Omega $

$\nabla \cdot p(x) - p\_s(x) + p\_t(x) = 0; \forall x \in \Omega $

Here $p(x)$ is a field vector and is analogous to the flow in the discrete domain. $\nabla \cdot p$ is the divergence of the field p.

How do i find out the dual of this maximization problem using the lagrangian dual technique, i.e. the equivalent min cut formulation of the problem in the continuous domain.

**Tags:** ds.algorithms, max-flow-min-cut, primal-dual

---

## 1 answers

### Answer by username_1 on 2011-06-07. Score: 1 | Accepted answer

Your question may be answered in the following paper:

@article{strang1983maximal,
title={Maximal flow through a domain},
author={Strang, G.},
journal={Mathematical Programming},
volume={26},
number={2},
pages={123--143},
year={1983},
publisher={Springer}
}

> **Comments:**
> **username_0**: The paper does not take the approach that i want to follow. I believe that the dual can be obtained by simply finding the lagrangian function. I just did not know how to find the lagrangian dual function for the given function. I have now worked it out.  

---

