| Article ID: | iaor19921837 |
| Country: | United States |
| Volume: | 17 |
| Issue: | 2 |
| Start Page Number: | 411 |
| End Page Number: | 443 |
| Publication Date: | May 1992 |
| Journal: | Mathematics of Operations Research |
| Authors: | Haussmann U.G. |
| Keywords: | programming: nonlinear |
The quadratic variation of Brownian motion is used to give a new definition of a generalized Hessian for nonsmooth functions, totally independently of any gradients. A calculus is developed for the generalized Hessian of functions whose gradient is Lipschitz. It is also shown that for convex functions the Hessian is nonempty.