Functions
void	Tut2_ModelData::buildModel ()
	adds the variables and constraints for the problem

int	Tut2_ModelData::FDEval (const double x[], double g, double jac[], int rowno, const int jacnum[], int mode, int ignerr, int errcnt, int numvar, int numjac, int thread)
	defines the nonlinearities of the model by returning numerical values.

int	Tut2_ModelData::SDLagrVal (const double x[], const double u[], const int hsrw[], const int hscl[], double hsvl[], int *nodrv, int numvar, int numcon, int nhess)
	Computes and returns the numerical values of the Hessian.

int	main (int argc, char **argv)
	Main program. A simple setup and call of CONOPT.

Detailed Description

This model is a revision of Tutorial in which we have added a set of 2nd derivative routines, Tut_2DLagrStr and Tut_2DLagrVal.

For more information about the individual callbacks, please have a look at the source code.

Function Documentation

◆ buildModel()

void Tut2_ModelData::buildModel ( )

inline

adds the variables and constraints for the problem

Definition at line 26 of file tutorial2.cpp.

◆ FDEval()

int Tut2_ModelData::FDEval	(	const double	x[],
		double *	g,
		double	jac[],
		int	rowno,
		const int	jacnum[],
		int	mode,
		int	ignerr,
		int *	errcnt,
		int	numvar,
		int	numjac,
		int	thread )

inlinevirtual

defines the nonlinearities of the model by returning numerical values.

It must be defined by the modeler if the model is nonlinear. The routine is called repeatedly during the optimization so it should be implemented efficiently. Some arguments are provided by CONOPT. The remaining arguments must be defined by the modeler. Note that FDEval works on one row or equation at a time.

where:

X: Vector with the point of evaluation. The point is provided by CONOPT.
G: Scalar function value: The value of G must be returned by the modeler if MODE = 1 or 3, otherwise it will be ignored. If FVincLin defined in coidef_fvinclin() is 0, the default value, then G should return the sum of the nonlinear terms in row number ROWNO, and if FVincLin is 1 then G should return the sum of both linear and nonlinear terms. The nonlinear terms are defined as all terms that correspond to Jacobian elements with NLFLAG = 1 when loading the model. Constant terms in nonlinear constraints may be included in G provided RHS in ReadMatrix is adjusted correspondingly. Constant terms in linear constraints may also be defined here provided FVforAll is given the non default value 1 in coidef_fvforall(). In summary, G should include the following, depending on FVincLin and FVforAll:
```
| FVforAll \ FVincLin | 0 | 1 |
|---------------------|---|---|
| 0                   | G includes nonlinear terms only. FDEval is only called for nonlinear rows. | G includes linear and nonlinear terms. FDEval is only called for nonlinear rows. |
| 1                   | G includes nonlinear and constant terms. FDEval is called for all rows. | G includes linear, nonlinear, and constant terms. FDEval is called for all rows. |
```

JAC: Vector of Jacobian values. All the nonlinear Jacobian values in row number ROWNO (and only these) should be evaluated. The indices in JAC are the indices of the variables, i.e. the derivative with respect to X(I) should be returned in JAC(I). JAC must be returned by the modeler if MODE = 2 or 3; otherwise it must be ignored.
ROWNO: Scalar with the number of the row for which nonlinearities are to be evaluated. Is provided by CONOPT. Note that if FVforAll = 0, the default value, then FDEval will only be called for nonlinear rows, and constant terms in linear rows must therefore be included in RHS in ReadMatrix. If FVforAll = 1 then FDEval will be called for all rows, and the linear constraints must return any constant term that is not included in the right hand side. CONOPT will initialize G to zero so FDEval can just return for linear rows without constant terms. In summary, FDEval will be called for the following values of ROWNO, depending on FVforAll:
```
- <b>0:</b> Called for all nonlinear rows only.
- <b>1:</b> Called for all rows.

The row numbers are consistent with the Base selected by the modeler.
```

JCNM: Vector with a list of column numbers for the nonlinear nonzero Jacobian elements in the current row. It is only defined when MODE = 2 or 3. JCNM and NJ are provided for modelers that may find this information useful; it can be ignored by others. The numbers are consistent with the Base (Fortran or C conventions) selected by the modeler.
MODE: Scalar indicator for mode of evaluation, provided by CONOPT:
- 1: Only evaluate the sum of the nonlinear terms (and possibly linear terms) in row ROWNO and return the value in G.
- 2: Only evaluate the nonlinear Jacobian elements in row ROWNO and return them in JAC.
- 3: Perform both option 1 and 2.
IGNERR: Scalar that indicates whether CONOPT assumes the point to be safe (0) or potentially unsafe (1). During certain parts of the optimization CONOPT will make very long steps and it is not unlikely that one of the constraints is not defined. If an error is encountered while IGNERR is 1, this error is not included in the ErrLim limit, and the modeler may skip any error messages that otherwise should be issued from FDEval.
ERRCNT: Scalar Function Evaluation Error Indicator. FDEval must set this argument to 1 each time a function value cannot be computed. The counts are accumulated by CONOPT (except when IGNERR = 1). If their sum exceeds the ErrLim value defined in coidef_errlim(), CONOPT will stop the optimization, communicate the solution to the modeler with solver status SOLSTA = 5 (Evaluation Error Limit) in callback routine Status, and return control to the modeler. If ERRCNT has been set by FDEval then G and JAC will not be used and CONOPT will in general try to backtrack to a "safe" point. Note that CONOPT assumes that all functions are defined for all values of the variables between their bounds. CONOPT will never call FDEval with X outside the bounds specified in ReadMatrix. Also see the Progress callback routine for an alternative way of stopping CONOPT.
NEWPT: Scalar new point indicator, provided by CONOPT:
- 0: This is the same point as in last call, i.e. ROWNO has changed but the nonlinear variables in X have not changed. Some variables that are linear in all constraints may also have been changed.
- 1: This is a new point.
NEWPT is provided by CONOPT as a service to the modeler. It may be used to calculate and reuse terms that depend on X but are common among several equations, e.g. when some of the equations represent simultaneous sets of differential equations solved by an expensive integration routine.
N: Number of variables as defined in coidef_numvar().
NJ: Number of nonlinear nonzero Jacobian elements in the current row and number of elements in the JCNM vector. JCNM is only defined when MODE = 2 or 3; when MODE = 1 then NJ has the value 1 and JCNM points to a random vector.
THREAD: In some multi-threading environments multiple copies of FDEval can be called at the same time, (see Multi Threading). THREAD will hold the number of the thread for the current call of FDEval. THREAD is in the interval from 0 to the maximum number of threads allowed for FDEval.
USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API).

You should notice the difference between the ERRCNT and the return code of FDEval. A nonzero value returned in ERRCNT indicates that the current point defined in X is bad. The function value G or the derivatives JAC could not be computed and CONOPT should try to backtrack to a safe point. A nonzero value returned as the value of FDEval indicates that there is a serious or permanent error and there is no reason to continue the optimization. The return code on FDEval can for example be used if a data file is not found, or if FDEval is called with a value of ROWNO that was not expected.

Reimplemented from ConoptModelData.

Definition at line 86 of file tutorial2.cpp.

◆ SDLagrVal()

int Tut2_ModelData::SDLagrVal	(	const double	x[],
		const double	u[],
		const int	hsrw[],
		const int	hscl[],
		double	hsvl[],
		int *	nodrv,
		int	numvar,
		int	numcon,
		int	nhess )

inlinevirtual

Computes and returns the numerical values of the Hessian.

The structure of the Lagrangian of the Hessian is provided using setSDLagrangianStructure()

where:

MODE: Distinguishes between the three modes described above.
X: Vector with the point in which the Hessian of the Lagrangian should be computed. Defined by CONOPT when MODE = 3.
U: The vector of weights on the individual constraints. The Lagrangian is defined as L = SUM(r in rows)U(r) . function(r). U is defined by CONOPT when MODE = 3.
ROWNO: Vector of row numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3.
COLNO: Vector of column numbers of the lower triangular part of the Hessian. Must be defined by the modeler when MODE = 2 and is provided as a help to the modeler when MODE = 3. The elements of the Hessian must be sorted column wise, i.e. COLNO must be non-decreasing. Within each column the elements must be sorted row-wise, i.e. the elements of ROWNO must be increasing for sequences for which COLNO is constant. The row and column numbers are interpreted according to Base, i.e. they are between 1 and N when Base = 1 (Fortran conventions) and between 0 and N-1 when Base = 0 (C conventions).
VALUE: Vector returning the values of the second derivatives when MODE = 3. The individual elements must be defined in the order used for ROWNO and COLNO. VALUE will be initialized to zero when 2DLagrVal is called and it must be defined by the modeler.
NODRV: Can be set to 1 if the derivatives for some reason could not be computed, for example because some of them were not defined. Is initialized to 0 by CONOPT. CONOPT will not use second order methods in the current point if NODRV is 1.
N: The number of variables in the model as defined in coidef_numvar(). Provided by CONOPT.
M: The number of constraints in the model as defined in coidef_numcon(). Provided by CONOPT.
NHESS: The number of nonzero elements in the Hessian. When MODE = 1 CONOPT will define the maximum number of elements it will accept in NHESS, and 2DLagrVal must return the actual number of element. If the actual number is larger than the input value of NHESS then CONOPT will not use the Hessian of the Lagrangian and 2DLagrVal will not be called again. When MODE > 1 NHESS is defined by CONOPT as the value provided by the modeler in the first call.
USRMEM: User memory as defined in coidef_usrmem() (Only for Fortran and C API).

2DLagrVal will only be called in points in which the constraint values have been computed successfully before with FDEval. Checks for function evaluation errors can therefore usually be limited. Note that 2DLagrVal in some cases can be called in a point that is different from the last point in which FDEval was called.

The maximum number of Hessian nonzero elements accepted by CONOPT is computed as the option value RVHESS multiplied by the number of nonlinear Jacobian elements. The default value of RVHESS is 10. If the Hessian has more than 10 times as many elements as the Jacobian it is expected that it is too expensive to compute and that directional 2^nd derivatives in some form are more efficient to use. The modeler may allow CONOPT to use a denser Hessian by increasing RVHESS.

There is a rudimentary debugger of the values returned by 2DLagrVal. It can be turned on by setting Debug2D in coidef_debug2d() or with the option LKDEB2. Information on the debugger including messages and error return codes can be found in Error Return Codes.

Reimplemented from ConoptModelData.

Definition at line 167 of file tutorial2.cpp.

◆ main()

int main	(	int	argc,
		char **	argv )

Main program. A simple setup and call of CONOPT.