# D'Onofrio model (binary variant)

D'Onofrio model (binary variant) | |
---|---|

State dimension: | 1 |

Differential states: | 4 |

Discrete control functions: | 4 |

Path constraints: | 2 |

This site describes a D'Onofrio model variant with four binary controls instead which of only two continuous controls. The continuous controls are replaced via the outer convexifacation method.

## Mathematical formulation

For the optimal control problem is given by

## Parameters

The parameters and scenarios are as in D'Onofrio_chemotherapy_model, the new fixed parameters are

## Reference Solutions

If the problem is relaxed, i.e., we demand that be in the continuous interval instead of the binary choice , the optimal solution can be determined by using a direct method such as collocation or Bock's direct multiple shooting method.

The optimal objective value of scenario 2 of the relaxed problem with is . The objective value of the binary controls obtained by Combinatorial Integral Approimation (CIA) is . The binary control solution was evaluated in the MIOCP by using a Merit function with additional Mayer term
.

## Source Code

Model description is available in