The \(h\) function

The function \(h : \mathbf{R}^p\to\mathbf{R}\cup\{\infty\}\) is separable down to the component and is piecewise linear in each component. The figure shows a 1-dimensional example. The function can model, e.g.,:

  • Hard constraints (if slopes are infinite)
  • Soft constraints (if finite slope)
  • The 1-norm