R/175_reductions_dcp2cone_canonicalizers_quad_huber_canon.R

In CVXR: Disciplined Convex Optimization

#####
## DO NOT EDIT THIS FILE!! EDIT THE SOURCE INSTEAD: rsrc_tree/reductions/dcp2cone/canonicalizers/quad/huber_canon.R
#####

## CVXPY SOURCE: reductions/dcp2cone/canonicalizers/quad/huber_canon.py
## huber(x, M) = n^2 + 2*M*|s| where x = s + n
## Uses power_quad_canon for n^2 (produces SymbolicQuadForm)
## and abs_canon for |s| (produces linear + constraints)


huber_quad_canon <- function(expr, args, solver_context = NULL) {
  M <- expr@M
  x <- args[[1L]]
  shape <- expr@shape
  n <- Variable(shape = shape)
  s <- Variable(shape = shape)

  ## n^2 via power_quad_canon -> SymbolicQuadForm
  power_expr <- power(n, 2)
  n2_result <- power_quad_canon(power_expr, power_expr@args)
  n2 <- n2_result[[1L]]
  constr_sq <- n2_result[[2L]]

  ## |s| via abs_canon (linear + constraints)
  abs_expr <- Abs(s)
  abs_result <- abs_canon(abs_expr, abs_expr@args)
  abs_s <- abs_result[[1L]]
  constr_abs <- abs_result[[2L]]

  obj <- n2 + 2 * M * abs_s

  ## x == s + n
  constraints <- c(constr_sq, constr_abs, list(x == s + n))
  list(obj, constraints)
}

method(quad_canonicalize, Huber) <- huber_quad_canon