gams:model_piecewise_linear_functions

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gams:model_piecewise_linear_functions [2007/10/20 07:52] Franz Nelissen |
gams:model_piecewise_linear_functions [2009/10/27 13:59] (current) support |
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CONOPT like smooth continuous-differentiable functions). | CONOPT like smooth continuous-differentiable functions). | ||

- | In fact the piecewise linear function you describe can be modeled with some MIP solvers using socalled SOS 2 variables, or with general binary variables. Check textbooks like Nemhauser and Wolsey, Integer and Combinatorial Optimization (page 10) and H.P. Williams, Model Building in Mathematical Programming (section 7.3,9.3) for more information. | + | In fact the piecewise linear function you describe can be modeled with some MIP solvers using socalled SOS 2 variables, or with general binary variables. Check textbooks like Nemhauser and Wolsey, Integer and Combinatorial Optimization (page 10) and H.P. Williams, Model Building in Mathematical Programming (section 7.3,9.3) for more information. Some examples are collected [[gams:linearize_a_non-linear_function |here]]. |

Sometimes the following trick can be used: if you are minimizing Q one can introduce the inequalities: q >= aP+b q >= cP+d q >= eP+f because of the form of the P-Q curve. [here a picture approximately | Sometimes the following trick can be used: if you are minimizing Q one can introduce the inequalities: q >= aP+b q >= cP+d q >= eP+f because of the form of the P-Q curve. [here a picture approximately |

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