SOLNP – Nonlinear optimization solver

Block SymbolLicensing group: MATRIX

Function Description
The SOLNP block is designed to solve a general Nonlinear Programming Problem (NLP) in the form

min f (x)

subject to

\begin{array}{l} g (x) & = 0, \\ l_{h} & \leq h (x) \leq u_{h}, \\ l_{x} & \leq x \leq u_{x}, \end{array}

where

$x \in ℝ^{n}$ is a vector of decision variables to be optimized,
$f (x)$ is a cost function (objective function),
$g (x)$ is a vector of equality constraints,
$h (x)$ is a vector of inequality constraints,
$l_{h}$ is a vector of lower bounds on inequality constraints,
$u_{h}$ is a vector of upper bounds on inequality constraints,
$l_{x}$ is a vector of lower bounds on decision variables,
$u_{x}$ is a vector of upper bounds on decision variables.

The SOLNP solver tries to find optimal solution $x^{*} = \underset{x}{arg min} f (x)$ with the use of Augmented Lagrangian Method and Sequential Quadratic Programming (SQP).

For technical details, refer to [16] and [17]. In general, $f$ , $g$ , and $h$ are any nonlinear smooth functions.

Regarding implementation, the objective function, equality, and inequality constraints can be defined separately, for example, via the REXLANG block which allows the definition of custom functions. Its output y0 is then propagated back to SOLNP’s input uBlk.

The following auxiliary variables may be used in the formulation of the optimization problem to be solved by SOLNP block:

Vector of initial estimates: $x_{0}$ .
Matrix $x_{b}$ defining range of decision variables, referred to as simple bounds: $x_{b} = [l_{x}, u_{x}]$ .
Matrix $u I b$ defining inequality constraints: $u I b = [l_{h}, u_{h}]$ (optional, only used if the optimization problem includes inequality constraints).

The block can be configured in one of three ways depending on how the input vector $u X b$ is constructed:

$u X b = [x_{0}, x_{b}]$ : The solver will use the given initial estimate and simple bounds.
$u X b = x_{0}$ : The solver will only use the given initial estimate.
$u X b = x_{b}$ : The solver only uses the given simple bounds. Initial estimate is constructed automatically as $x_{0} = \frac{l_{x} + u_{x}}{2}$ .

The vector $u X b$ may have one, two, or three columns; and the number of rows corresponds to the number of decision variables (dimension of $x$ ).

This block does not propagate the signal quality. More information can be found in the 1.4 section.

Input

uBlk	Associated REXLANG block reference	Reference
uXb	Initial estimate and simple bounds	Reference
uIb	Bounds on inequality constraints (optional)	Reference
uHes	User-supplied Hessian matrix (optional)	Reference
HLD	Hold	Bool

Parameter

rho	Penalty parameter for the augmented Lagrangian objective function $⊙$ 1.0	Double (F64)
MaxIterMajor	Maximum number of major iterations $↓$ 0 $⊙$ 400	Long (I32)
MaxIterMinor	Maximum number of minor iterations $↓$ 0 $⊙$ 200	Long (I32)
delta	Perturbation parameter for numerical gradient calculation $↓$ 1.79769e+308 $↑$ double	Long (I32)
tolerance	Tolerance parameter for feasibility and optimality $↓$ 1.79769e+308 $↑$ double	Long (I32)
nmax	Allocated size of array $↓$ 10 $↑$ 100000 $⊙$ 100	Long (I32)

Output

cmd	Phase identification for the associated REXLANG block	Long (I32)
yX	Input vector for the associated REXLANG block	Reference
yF	Output vector for the associated REXLANG block	Reference
E	Error indicator	Bool
iE	Error code	Long (I32)

[Previous] [Back to top] [Up]