| Article ID: | iaor20003638 |
| Country: | Singapore |
| Volume: | 16 |
| Issue: | 1 |
| Start Page Number: | 53 |
| End Page Number: | 62 |
| Publication Date: | May 1999 |
| Journal: | Asia-Pacific Journal of Operational Research |
| Authors: | Craven B.D. |
| Keywords: | programming: convex, programming: multiple criteria |
An optimal control problem is studied, with several objective functions, which considers a weak (or Pareto) minimum. A version of Pontryagin’s principle is shown to hold, involving a weak minimum of a vector Hamiltonian with respect to the control, as well as a generalized adjoint differential equation. These necessary conditions become sufficient under additional invex hypotheses on the functions; and duality results also hold.