solnp_standardize_problem: Standardize an Optimization Problem to NLP Standard Form

Description

Converts a problem specified with two-sided inequalities and nonzero equality right-hand sides to the standard nonlinear programming (NLP) form.

Usage

solnp_standardize_problem(prob)

Value

A list with the same structure as the input, but with eq_fn and ineq_fn

standardized to the forms $e(x) = 0$ and $g(x) \leq 0$, and with eq_b, ineq_lower, and ineq_upper removed.

Arguments

prob: A list specifying the problem in SOLNP-compatible format, with components fn, eq_fn, eq_jac, eq_b, ineq_fn, ineq_jac, ineq_lower, ineq_upper, and others.

Details

The standard form given by the following set of equations:

$$ \min_x\ f(x) $$ $$ \textrm{subject to}\quad e(x) = 0 $$ $$ \qquad\qquad\qquad g(x) \leq 0 $$

Specifically:

All equality constraints are standardized to $e(x) = e(x) - b = 0$
Each two-sided inequality $l \leq g(x) \leq u$ is converted to one or two one-sided constraints: $l - g(x) \leq 0$, $g(x) - u \leq 0$

The returned problem object has all equalities as $e(x) = 0$, all inequalities as $g(x) \leq 0$, and any right-hand side or bounds are absorbed into the standardized constraint functions.

Examples

Run this code

# Alkylation problem
p <- solnp_problem_suite(suite = "Other", number = 1)
ps <- solnp_standardize_problem(p)
ps$eq_fn(ps$start)    # standardized equalities: e(x) = 0
ps$ineq_fn(ps$start)  # standardized inequalities: g(x) <= 0