# Hanging chain problem (TACO)

From mintOC

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

- Mathematical notation at Hanging chain problem
- AMPL (using a fixed discretization) at the COPS library