# Hanging chain problem (TACO)

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This page contains a model of the Hanging chain problem in AMPL format, making use of the TACO toolkit for AMPL control optimization extensions. The original model using a collocation formulation can be found in the COPS library. Note that you will need to include a generic AMPL/TACO support file, OptimalControl.mod. To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

### AMPL

This is the source file hangchain_taco.mod

```# ----------------------------------------------------------------
# Hanging chain problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
#
# Source: COPS 3.1 collocation formulation - March 2004
#         Alexander S. Bondarenko - Summer 1998
# ----------------------------------------------------------------
include OptimalControl.mod;

var t;
var tf := 1;

var x >= 0, <= 10;
var L >= 0, <= 10;
var E >= 0, <= 10;
var u >= -10, <= 20 suffix type "u1";

param a := 1;
param b := 3;
param Lp := 4;

minimize energy: eval(E,tf);

subject to

dx: diff(x,t) = u;
dE: diff(E,t) = x*sqrt(1+u^2);
dL: diff(L,t) = sqrt(1+u^2);

x0: eval(x,0) = a;
x1: eval(x,1) = b;
E0: eval(E,0) = 0;
L0: eval(L,0) = 0;
L1: eval(L,1) = Lp;

option solver ...;

solve;```

## Other Descriptions

Other descriptions of this problem are available in