Article ID: | iaor20119953 |
Volume: | 51 |
Issue: | 3 |
Start Page Number: | 395 |
End Page Number: | 412 |
Publication Date: | Nov 2011 |
Journal: | Journal of Global Optimization |
Authors: | Sun Jie, Jiang Yi, He Ran |
Keywords: | control, programming: linear, programming: multiple criteria |
We present several formulae for the proximal and Fréchet subdifferentials of the minimal time function defined by a linear control system and a target set. At every point inside the target set, the proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of the target set and an upper level set of a so‐called Hamiltonian function which depends only on the linear control system. At every point outside the target set, under a mild assumption, proximal/Fréchet subdifferential is the intersection of the proximal/Fréchet normal cone of an enlargement of the target set and a level set of the Hamiltonian function.