solnp: Nonlinear optimization using augmented Lagrange method...

In Rsolnp: General Non-Linear Optimization

Nonlinear optimization using augmented Lagrange method (original version)

Description

Nonlinear optimization using augmented Lagrange method (original version)

Usage

solnp(
  pars,
  fun,
  eqfun = NULL,
  eqB = NULL,
  ineqfun = NULL,
  ineqLB = NULL,
  ineqUB = NULL,
  LB = NULL,
  UB = NULL,
  control = list(),
  ...
)

Arguments

pars	an numeric vector of decision variables (length n).
fun	the objective function (must return a scalar).
eqfun	an optional function for calculating equality constraints.
eqB	a vector of the equality bounds (if eq_fn provided).
ineqfun	an optional function for calculating inequality constraints.
ineqLB	the lower bounds for the inequality (must be finite)
ineqUB	the upper bounds for the inequalitiy (must be finite)
LB	lower bounds on decision variables
UB	upper bounds on decision variables
control	a list of solver control parameters (see details).
...	additional arguments passed to the supplied functions (common to all functions supplied).

Details

The optimization problem solved by csolnp is formulated as:

\begin{aligned} \min_{x \in \mathbb{R}^n} \quad & f(x) \\ \text{s.t.} \quad & g(x) = b \\ & h_l \le h(x) \le h_u\\ & x_l \le x \le x_u\\ \end{aligned}

where f(x) is the objective function, g(x) is the vector of equality constraints with target value b, h(x) is the vector of inequality constraints bounded by h_l and h_u, with parameter bounds x_l and x_u. Internally, inequality constraints are converted into equality constraints using slack variables and solved using an augmented Lagrangian approach. The control is a list with the following options:

rho

This is used as a penalty weighting scaler for infeasibility in the augmented objective function. The higher its value the more the weighting to bring the solution into the feasible region (default 1). However, very high values might lead to numerical ill conditioning or significantly slow down convergence.

outer.iter

Maximum number of major (outer) iterations (default 400).

inner.iter

Maximum number of minor (inner) iterations (default 800).

delta

Relative step size in forward difference evaluation (default 1.0e-7).

tol

Relative tolerance on feasibility and optimality (default 1e-8).

trace

The value of the objective function and the parameters is printed at every major iteration (default 1).

Value

An list with the following slot:

pars

Optimal Parameters.

convergence

Indicates whether the solver has converged (0) or not (1 or 2).

values

Vector of function values during optimization with last one the value at the optimal.

lagrange

The vector of Lagrange multipliers.

hessian

The Hessian of the augmented problem at the optimal solution.

ineqx0

The estimated optimal inequality vector of slack variables used for transforming the inequality into an equality constraint.

nfuneval

The number of function evaluations.

elapsed

Time taken to compute solution.

Author(s)

Alexios Galanos

Examples

{
# From the original paper by Y.Ye
# see the unit tests for more....
# POWELL Problem
fn1 = function(x)
{
    exp(x[1] * x[2] * x[3] * x[4] * x[5])
}
eqn1 = function(x){
    z1 = x[1] * x[1] + x[2] * x[2] + x[3] * x[3] + x[4] * x[4] + x[5] * x[5]
    z2 = x[2] * x[3] - 5 * x[4] * x[5]
    z3 = x[1] * x[1] * x[1] + x[2] * x[2] * x[2]
    return(c(z1, z2, z3))
}
x0 = c(-2, 2, 2, -1, -1)
}
powell = solnp(x0, fun = fn1, eqfun = eqn1, eqB = c(10, 0, -1))

Rsolnp documentation built on June 20, 2025, 5:07 p.m.