| Article ID: | iaor20108149 |
| Volume: | 147 |
| Issue: | 3 |
| Start Page Number: | 419 |
| End Page Number: | 442 |
| Publication Date: | Dec 2010 |
| Journal: | Journal of Optimization Theory and Applications |
| Authors: | Malinowska B, Torres M |
| Keywords: | optimization |
We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.