# Lotka Volterra absolute fishing problem

Lotka Volterra absolute fishing problem | |
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State dimension: | 1 |

Differential states: | 3 |

Discrete control functions: | 5 |

Interior point equalities: | 3 |

This site describes a Lotka Volterra variant with five binary controls that all represent fishing of an absolute biomass.

## Mathematical formulation

The mixed-integer optimal control problem is given by

Here the differential states describe the biomasses of prey and predator, respectively. The third differential state is used here to transform the objective, an integrated deviation, into the Mayer formulation . This problem variant allows to choose between five different fishing options.

## Parameters

These fixed values are used within the model.

## Reference Solutions

If the problem is relaxed, i.e., we demand that is in the continuous interval rather than being binary, the optimal solution can be determined by means of direct optimal control.

The optimal objective value of the relaxed problem with is . The objective value of the solution with binary controls obtained by Combinatorial Integral Approximation (CIA) is .