Relating U-Lagrangians to Second-order Epi-derivatives and Proximal-tracks
Claudia Sagastizabal | Mifflin, Robert
U-Lagrangian | proximal point | second-order epi-derivatives.
We make use of $\V\U$-space decomposition theory to connect three min-\linebreak imization-oriented objects. These objects are $\U$-Lagrangians obtained from minimizing a function over $\V$-space, proximal points depending on minimization over $\Re^n=\U\oplus\V$, and epi-derivatives determined by lower limits associated with epigraphs. We relate second-order epi-derivatives of a function to the Hessian of its associated $\U$-Lagrangian. We also show that the function's proximal points are on a trajectory determined by certain $\V$-space minimizers.