partial_optimize: Partial optimization transform

Description

Builds an Expression representing the optimal value of prob as a function of the variables you choose NOT to optimise over. Useful for two-stage / hierarchical optimisation, custom atom definitions, and embedding sub-problems inside larger problems.

Usage

partial_optimize(
  prob,
  opt_vars = NULL,
  dont_opt_vars = NULL,
  solver = NULL,
  ...
)

Value

A PartialProblem expression.

Arguments

prob: A Problem to partially optimise.
opt_vars: Optional list of Variables to optimise over.
dont_opt_vars: Optional list of Variables to keep as free arguments of the resulting expression.
solver: Optional solver name (passed to psolve() when the PartialProblem is evaluated via value() or grad()).
...: Additional named arguments forwarded to psolve() when value() / grad() are called.

Details

Exactly one of opt_vars or dont_opt_vars may be NULL; the missing list is taken to be the complement (relative to the full list of variables in prob). If both are supplied, they must together cover every variable in prob.

The returned PartialProblem is an Expression with scalar shape: it is convex when prob is DCP with a Minimize objective and concave when DCP with Maximize. Embed it like any other expression in a larger Problem; the larger problem's canonicalizer will pull the inner objective and constraints into the outer cone form so a single solve handles both layers.

Examples

Run this code

if (FALSE) {
x <- Variable(3)
t <- Variable(3)
abs_x <- partial_optimize(
  Problem(Minimize(sum_entries(t)), list(-t <= x, x <= t)),
  opt_vars = list(t)
)
## abs_x is now an expression of x alone, equivalent to sum(abs(x)).
}