# NLPQLP

NLPQLP is a sequential quadratic programming (SQP) method which solves problems with smooth continuously differentiable objective function and constraints. The algorithm uses a quadratic approximation of the Lagrangian function and a linearization of the constraints. To generate a search direction a quadratic subproblem is formulated and solved. The line search can be performed with respect to two alternative merit functions, and the Hessian approximation is updated by a modified BFGS formula.

NLPQLP is a proprietary software, which can be obtained here. The supported versions are v4.2.2 and v5.0.3, but other versions may work.

## Options

NLPQLP Default Options

Name

Type

Default value

Description

`accuracy`

float

1e-06

Convergence accuracy

`accuracyQP`

float

1e-14

Convergence accuracy for QP

`stepMin`

float

1e-06

Minimum step length

`maxFun`

int

20

Maximum Number of Function Calls During Line Search

`maxIt`

int

500

Maximum Number of Iterations

`maxNM`

int

1

Maximum stack size for non-monotone line search

`rho`

float

1.0

Factor scaling identify for IFAIL=2

`iPrint`

int

2

Output Level

• `2`: Major

• `0`: None

• `1`: Final

• `3`: Major/Minor

• `4`: Full

`mode`

int

0

Mode (0 - Normal Execution, 1 to 18 - See Manual)

`iOut`

int

6

Output Unit Number

`lMerit`

bool

True

Merit Function Type (True - L2 Augmented Penalty, False - L1 Penalty)

`lQl`

bool

False

QP Subproblem Solver (True - Quasi-Newton, False - Cholesky)

`iFile`

str

`NLPQLP.out`

Output File Name

## Informs

NLPQLP Informs

Code

Description

`-2`

Compute gradient values w.r.t. the variables stored in first column of X, and store them in DF and DG. Only derivatives for active constraints ACTIVE(J)=.TRUE. need to be computed.

`-1`

Compute objective fn and all constraint values subjectthe variables found in the first L columns of X, and store them in F and G.

`0`

The optimality conditions are satisfied.

`1`

The algorithm has been stopped after MAXIT iterations.

`2`

The algorithm computed an uphill search direction.

`3`

Underflow occurred when determining a new approximation matrix for the Hessian of the Lagrangian.

`4`

The line search could not be terminated successfully.

`5`

Length of a working array is too short. More detailed error information is obtained with IPRINT>0

`6`

There are false dimensions, for example M>MMAX, N>=NMAX, or MNN2<>M+N+N+2.

`7`

The search direction is close to zero, but the current iterate is still infeasible.

`8`

The starting point violates a lower or upper bound.

`9`

Wrong input parameter, i.e., MODE, LDL decomposition in D and C (in case of MODE=1), IPRINT, IOUT

`10`

Internal inconsistency of the quadratic subproblem, division by zero.

`11`

More than MAXFUN successive non-evaluable function calls.

`100`

The solution of the quadratic programming subproblem has been terminated with an error message and IFAIL is set to IFQL+100, where IFQL denotes the index of an inconsistent constraint.

## API

class pyoptsparse.pyNLPQLP.pyNLPQLP.NLPQLP(*args, **kwargs)[source]

NLPQL Optimizer Class - Inherited from Optimizer Abstract Class

This is the base optimizer class that all optimizers inherit from. We define common methods here to avoid code duplication.

Parameters:
namestr

Optimizer name

categorystr

Typically local or global

defaultOptionsdictionary

A dictionary containing the default options

informsdict

Dictionary of the inform codes

__call__(optProb, sens=None, sensStep=None, sensMode=None, storeHistory=None, hotStart=None, storeSens=True)[source]

This is the main routine used to solve the optimization problem.

Parameters:
optProbOptimization or Solution class instance

This is the complete description of the optimization problem to be solved by the optimizer

sensstr or python Function.

Specify method to compute sensitivities. To explicitly use pyOptSparse gradient class to do the derivatives with finite differences use ‘FD’. ‘sens’ may also be ‘CS’ which will cause pyOptSpare to compute the derivatives using the complex step method. Finally, ‘sens’ may be a python function handle which is expected to compute the sensitivities directly. For expensive function evaluations and/or problems with large numbers of design variables this is the preferred method.

sensStepfloat

Set the step size to use for design variables. Defaults to 1e-6 when sens is ‘FD’ and 1e-40j when sens is ‘CS’.

sensModestr

Use ‘pgc’ for parallel gradient computations. Only available with mpi4py and each objective evaluation is otherwise serial

storeHistorystr

File name of the history file into which the history of this optimization will be stored

hotStartstr

File name of the history file to “replay” for the optimization. The optimization problem used to generate the history file specified in ‘hotStart’ must be IDENTICAL to the currently supplied ‘optProb’. By identical we mean, EVERY SINGLE PARAMETER MUST BE IDENTICAL. As soon as he requested evaluation point from NLPQL does not match the history, function and gradient evaluations revert back to normal evaluations.

storeSensbool

Flag specifying if sensitivities are to be stored in hist. This is necessary for hot-starting only.