A general take on descent algorithms (2)

We consider here again the GPGD introduced in the first part i.e., the iteration

\[ \begin{eqnarray} x_{k+1} &=& \arg\min_{x\in C}\,\,\left\{\langle x,\nabla f(x_{k})\rangle + {1\over \alpha_{k}}d(x,x_{k})\right\} \end{eqnarray} \]

and discuss the choice of the positive-definite function \(d\).

1. Changing coordinates

(under construction)