int CPLEXAddConstraint(LinEquation* InEquation) {
int Status = 0;
if (InEquation->ConstraintType != QUADRATIC && InEquation->ConstraintType != LINEAR) {
FErrorFile() << "This constraint type is not supported in CPLEX: " << InEquation->ConstraintType << endl;
FlushErrorFile();
return FAIL;
}
//First I check the number of rows. If it's larger than the index, then this constraint already exists and is only being changed
int NumberRows = CPXgetnumrows (CPLEXenv, CPLEXModel);
if (NumberRows <= InEquation->Index) {
char* Sense = new char[1];
if (InEquation->EqualityType == EQUAL) {
if (InEquation->QuadOne.size() > 0) {
delete [] Sense;
FErrorFile() << "Quadratic constraints cannot be equivalent constraints in CPLEX." << endl;
FlushErrorFile();
return FAIL;
} else {
Sense[0] = 'E';
}
} else if (InEquation->EqualityType == LESS) {
Sense[0] = 'L';
} else if (InEquation->EqualityType == GREATER) {
Sense[0] = 'G';
} else {
delete [] Sense;
FErrorFile() << "Unrecognized constraint type: " << InEquation->ConstraintType << endl;
FlushErrorFile();
return FAIL;
}
double* Rhs = new double[1];
Rhs[0] = InEquation->RightHandSide;
int* ColInd = NULL;
int* RowInd = NULL;
double* Coeff = NULL;
if (InEquation->Variables.size() > 0) {
ColInd = new int[int(InEquation->Variables.size())];
RowInd = new int[int(InEquation->Variables.size())];
Coeff = new double[int(InEquation->Variables.size())];
for (int i=0; i < int(InEquation->Variables.size()); i++) {
Coeff[i] = InEquation->Coefficient[i];
RowInd[i] = 0;
ColInd[i] = InEquation->Variables[i]->Index;
}
}
if (InEquation->QuadOne.size() > 0) {
if (CPXgetprobtype(CPLEXenv, CPLEXModel) == CPXPROB_LP) {
Status = CPXchgprobtype(CPLEXenv, CPLEXModel, CPXPROB_QP);
}
else if (CPXgetprobtype(CPLEXenv, CPLEXModel) == CPXPROB_MILP) {
Status = CPXchgprobtype(CPLEXenv, CPLEXModel, CPXPROB_MIQP);
}
int *QuadCol = new int[int(InEquation->QuadOne.size())];
int *QuadRow = new int[int(InEquation->QuadTwo.size())];
double *QuadCoeff = new double[int(InEquation->QuadCoeff.size())];
for (int i=0; i < int(InEquation->QuadOne.size()); i++) {
QuadCol[i] = InEquation->QuadOne[i]->Index;
QuadRow[i] = InEquation->QuadTwo[i]->Index;
QuadCoeff[i] = InEquation->QuadCoeff[i];
}
Status = CPXaddqconstr(CPLEXenv, CPLEXModel, int(InEquation->Variables.size()), int(InEquation->QuadOne.size()), Rhs[0], int(Sense[0]), ColInd, Coeff, QuadRow, QuadCol, QuadCoeff, NULL);
delete [] QuadCol;
delete [] QuadRow;
delete [] QuadCoeff;
} else if (InEquation->Variables.size() > 0) {
string StrName = GetConstraintName(InEquation);
char** Name = new char*;
Name[0] = new char[StrName.length()+1];
strcpy(Name[0],StrName.data());
if ((InEquation->ConstraintMeaning.compare("chemical potential constraint") == 0) && (InEquation->Loaded == false) && (GetParameter("Check potential constraints feasibility").compare("1") == 0)) {
Rhs[0] = InEquation->LoadedRightHandSide;
Sense[0] = 'L';
} else if ((InEquation->ConstraintMeaning.compare("chemical potential constraint") == 0) && (InEquation->Loaded == false) && (InEquation->RightHandSide > 0.9*FLAG)){
Rhs[0] = FLAG;
Sense[0] = 'L';
}
Status = CPXaddrows(CPLEXenv, CPLEXModel, 0, 1, int(InEquation->Variables.size()), Rhs, Sense, RowInd, ColInd, Coeff, NULL, Name);
delete [] Name[0];
delete [] Name;
delete [] ColInd;
delete [] RowInd;
delete [] Coeff;
}
delete [] Rhs;
delete [] Sense;
if (Status) {
FErrorFile() << "Failed to add constraint: " << InEquation->Index << endl;
FlushErrorFile();
return FAIL;
}
} else {
if (InEquation->QuadOne.size() > 0) {
FErrorFile() << "Cannot change a quadratic constraint." << endl;
FlushErrorFile();
return FAIL;
} else {
int NumberOfColumns = CPXgetnumcols(CPLEXenv, CPLEXModel);
//First I reset all of the coefficients to zero
for (int i=0; i < NumberOfColumns; i++) {
Status = CPXchgcoef (CPLEXenv, CPLEXModel, InEquation->Index, i, 0);
if (Status) {
FErrorFile() << "Failed to change constraint: " << InEquation->Index << endl;
FlushErrorFile();
return FAIL;
}
}
//Next I set all of the nonzero coefficients according to the input equation
for (int i=0; i < int(InEquation->Variables.size()); i++) {
Status = CPXchgcoef (CPLEXenv, CPLEXModel, InEquation->Index, InEquation->Variables[i]->Index, InEquation->Coefficient[i]);
if (Status) {
FErrorFile() << "Failed to change constraint: " << InEquation->Index << endl;
FlushErrorFile();
return FAIL;
}
}
char* Sense = new char[1];
if (InEquation->ConstraintMeaning.compare("chemical potential constraint") == 0 && InEquation->Loaded == false) {
Sense[0] = 'L';
Status = CPXchgcoef (CPLEXenv, CPLEXModel, InEquation->Index, -1, InEquation->LoadedRightHandSide);
Status = CPXchgsense (CPLEXenv, CPLEXModel, 1, &(InEquation->Index), Sense);
} else {
//Now I change the RHS of the constraint
Status = CPXchgcoef (CPLEXenv, CPLEXModel, InEquation->Index, -1, InEquation->RightHandSide);
//Also change the sense of the constraint if nec
if (InEquation->EqualityType == EQUAL) {
if (InEquation->QuadOne.size() > 0) {
delete [] Sense;
FErrorFile() << "Quadratic constraints cannot be equivalent constraints in CPLEX." << endl;
FlushErrorFile();
return FAIL;
} else {
Sense[0] = 'E';
}
} else if (InEquation->EqualityType == LESS) {
Sense[0] = 'L';
} else if (InEquation->EqualityType == GREATER) {
Sense[0] = 'G';
} else {
delete [] Sense;
FErrorFile() << "Unrecognized constraint type: " << InEquation->ConstraintType << endl;
FlushErrorFile();
return FAIL;
}
Status = CPXchgsense (CPLEXenv, CPLEXModel, 1, &(InEquation->Index), Sense);
if (Status) {
FErrorFile() << "Failed to change constraint: " << InEquation->Index << endl;
FlushErrorFile();
return FAIL;
}
}
}
}
return SUCCESS;
}
/* This function creates the following model:
* Minimize
* obj: x1 + x2 + x3 + x4 + x5 + x6
* Subject To
* c1: x1 + x2 + x5 = 8
* c2: x3 + x5 + x6 = 10
* q1: [ -x1^2 + x2^2 + x3^2 ] <= 0
* q2: [ -x4^2 + x5^2 ] <= 0
* Bounds
* x2 Free
* x3 Free
* x5 Free
* End
* which is a second order cone program in standard form.
* The function returns a true value on success and false on error.
* The function also sets up *cone_p as follows:
* (*cone_p)[j] >= 0 Column j is contained in a cone constraint
* and is the cone head variable of that
* constraint. The index of the respective
* quadratic constraint is given by (*cone_p)[j].
* (*cone_p)[j] = NOT_CONE_HEAD Column j is contained in a cone constraint
* but is not the cone head variable of that
* constraint.
* (*cone_p)[j] = NOT_IN_CONE Column j is not contained in any cone
* constraint.
*/
static int
createmodel (CPXENVptr env, CPXLPptr lp, int **cone_p)
{
/* Column data. */
static double const obj[] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
static double const lb[] = { 0.0, -INF, -INF, 0.0, -INF, 0.0 };
static double const ub[] = { INF, INF, INF, INF, INF, INF };
static char const *const cname[] = { "x1", "x2", "x3", "x4", "x5", "x6" };
/* Row data. */
static double const rval[] = { 1.0, 1.0, 1.0, 1.0, 1.0, 1.0 };
static int const rind[] = { 0, 1, 4, 2, 4, 5 };
static int const rbeg[] = { 0, 3 };
static double const rhs[] = { 8.0, 10.0 };
static char const sense[] = { 'E', 'E' };
static char const *const rname[] = { "c1", "c2" };
/* Data for second order cone constraints. */
static double const qval[] = { -1.0, 1.0, 1.0 }; /* Same for all Q cons. */
static double const qrhs = 0.0; /* Same for all Q cons. */
static char const qsense = 'L'; /* Same for all Q cons. */
static int const qind1[] = { 0, 1, 2 };
static int const qind2[] = { 3, 4 };
int status;
int ok = 0;
int *cone = NULL;
CPXCHANNELptr errc;
/* Get the channel for printing error messages. */
if ( (status = CPXgetchannels (env, NULL, NULL, &errc, NULL)) != 0 )
goto TERMINATE;
cone = malloc ((sizeof (obj) / sizeof (obj[0])) * sizeof (*cone));
if ( cone == NULL ) {
CPXmsg (errc, "Out of memory!\n");
goto TERMINATE;
}
status = CPXchgobjsen (env, lp, CPX_MIN);
if ( status != 0 )
goto TERMINATE;
status = CPXnewcols (env, lp, sizeof (obj) / sizeof (obj[0]),
obj, lb, ub, NULL, (char **)cname);
if ( status != 0 )
goto TERMINATE;
status = CPXaddrows (env, lp, 0, sizeof (rhs) / sizeof (rhs[0]),
sizeof (rval) / sizeof (rval[0]), rhs, sense,
rbeg, rind, rval, NULL, (char **)rname);
if ( status != 0 )
goto TERMINATE;
status = CPXaddqconstr (env, lp, 0, sizeof (qind1) / sizeof (qind1[0]),
qrhs, qsense, NULL, NULL,
qind1, qind1, qval, "q1");
if ( status != 0 )
goto TERMINATE;
cone[0] = 0;
cone[1] = NOT_CONE_HEAD;
cone[2] = NOT_CONE_HEAD;
status = CPXaddqconstr (env, lp, 0, sizeof (qind2) / sizeof (qind2[0]),
qrhs, qsense, NULL, NULL,
qind2, qind2, qval, "q2");
if ( status != 0 )
goto TERMINATE;
cone[3] = 1;
cone[4] = NOT_CONE_HEAD;
cone[5] = NOT_IN_CONE;
ok = 1;
TERMINATE:
if ( !ok )
free (cone);
*cone_p = cone;
return ok;
}
int
main (void)
{
/* Declare pointers for the variables and arrays that will contain
the data which define the LP problem. The setproblemdata() routine
allocates space for the problem data. */
char *probname = NULL;
int numcols;
int numrows;
int objsen;
double *obj = NULL;
double *rhs = NULL;
char *sense = NULL;
int *matbeg = NULL;
int *matcnt = NULL;
int *matind = NULL;
double *matval = NULL;
double *lb = NULL;
double *ub = NULL;
int *qmatbeg = NULL;
int *qmatcnt = NULL;
int *qmatind = NULL;
double *qmatval = NULL;
int *qconrow = NULL;
int *qconcol = NULL;
double *qconval = NULL;
/* Declare and allocate space for the variables and arrays where we
will store the optimization results including the status, objective
value, variable values, dual values, row slacks and variable
reduced costs. */
int solstat;
double objval;
double x[NUMCOLS];
double slack[NUMROWS];
CPXENVptr env = NULL;
CPXLPptr lp = NULL;
int status;
int j;
int cur_numcols;
/* Initialize the CPLEX environment */
env = CPXopenCPLEX (&status);
/* If an error occurs, the status value indicates the reason for
failure. A call to CPXgeterrorstring will produce the text of
the error message. Note that CPXopenCPLEX produces no output,
so the only way to see the cause of the error is to use
CPXgeterrorstring. For other CPLEX routines, the errors will
be seen if the CPXPARAM_ScreenOutput indicator is set to CPX_ON. */
if ( env == NULL ) {
char errmsg[CPXMESSAGEBUFSIZE];
fprintf (stderr, "Could not open CPLEX environment.\n");
CPXgeterrorstring (env, status, errmsg);
fprintf (stderr, "%s", errmsg);
goto TERMINATE;
}
/* Turn on output to the screen */
status = CPXsetintparam (env, CPXPARAM_ScreenOutput, CPX_ON);
if ( status ) {
fprintf (stderr,
"Failure to turn on screen indicator, error %d.\n", status);
goto TERMINATE;
}
/* Fill in the data for the problem. */
status = setproblemdata (&probname, &numcols, &numrows, &objsen, &obj,
&rhs, &sense, &matbeg, &matcnt, &matind,
&matval, &lb, &ub, &qmatbeg, &qmatcnt,
&qmatind, &qmatval, &qconrow, &qconcol, &qconval);
if ( status ) {
fprintf (stderr, "Failed to build problem data arrays.\n");
goto TERMINATE;
}
/* Create the problem. */
lp = CPXcreateprob (env, &status, probname);
/* A returned pointer of NULL may mean that not enough memory
was available or there was some other problem. In the case of
failure, an error message will have been written to the error
channel from inside CPLEX. In this example, the setting of
the parameter CPXPARAM_ScreenOutput causes the error message to
appear on stdout. */
if ( lp == NULL ) {
fprintf (stderr, "Failed to create problem.\n");
goto TERMINATE;
}
/* Now copy the LP part of the problem data into the lp. */
status = CPXcopylp (env, lp, numcols, numrows, objsen, obj, rhs,
sense, matbeg, matcnt, matind, matval,
lb, ub, NULL);
if ( status ) {
fprintf (stderr, "Failed to copy problem data.\n");
goto TERMINATE;
}
/* Now copy the quadratic objective. */
status = CPXcopyquad (env, lp, qmatbeg, qmatcnt, qmatind, qmatval);
if ( status ) {
fprintf (stderr, "Failed to copy quadratic matrix.\n");
goto TERMINATE;
}
/* Now add the quadratic constraint. */
status = CPXaddqconstr (env, lp, 0, NUMQCONNZ, 1.0, 'L',
NULL, NULL, qconrow, qconcol, qconval, NULL);
if ( status ) {
fprintf (stderr, "Failed to copy quadratic constraint.\n");
goto TERMINATE;
}
/* Optimize the problem and obtain solution. */
status = CPXbaropt (env, lp);
if ( status ) {
fprintf (stderr, "Failed to optimize QCP.\n");
goto TERMINATE;
}
status = CPXsolution (env, lp, &solstat, &objval, x, NULL, slack, NULL);
if ( status ) {
fprintf (stderr, "Failed to obtain solution.\n");
goto TERMINATE;
}
/* Write the output to the screen. */
printf ("\nSolution status = %d\n", solstat);
printf ("Solution value = %f\n\n", objval);
/* The size of the problem should be obtained by asking CPLEX what
the actual size is, rather than using what was passed to CPXcopylp.
cur_numcols stores the current number of columns. */
cur_numcols = CPXgetnumcols (env, lp);
for (j = 0; j < cur_numcols; j++) {
printf ("Column %d: Value = %10f\n", j, x[j]);
}
/* Finally, write a copy of the problem to a file. */
status = CPXwriteprob (env, lp, "qcpex1.lp", NULL);
if ( status ) {
fprintf (stderr, "Failed to write LP to disk.\n");
goto TERMINATE;
}
TERMINATE:
/* Free up the problem as allocated by CPXcreateprob, if necessary */
if ( lp != NULL ) {
status = CPXfreeprob (env, &lp);
if ( status ) {
fprintf (stderr, "CPXfreeprob failed, error code %d.\n", status);
}
}
/* Free up the CPLEX environment, if necessary */
if ( env != NULL ) {
status = CPXcloseCPLEX (&env);
/* Note that CPXcloseCPLEX produces no output,
so the only way to see the cause of the error is to use
CPXgeterrorstring. For other CPLEX routines, the errors will
be seen if the CPXPARAM_ScreenOutput indicator is set to CPX_ON. */
if ( status ) {
char errmsg[CPXMESSAGEBUFSIZE];
fprintf (stderr, "Could not close CPLEX environment.\n");
CPXgeterrorstring (env, status, errmsg);
fprintf (stderr, "%s", errmsg);
}
}
/* Free up the problem data arrays, if necessary. */
free_and_null ((char **) &probname);
free_and_null ((char **) &obj);
free_and_null ((char **) &rhs);
free_and_null ((char **) &sense);
free_and_null ((char **) &matbeg);
free_and_null ((char **) &matcnt);
free_and_null ((char **) &matind);
free_and_null ((char **) &matval);
free_and_null ((char **) &lb);
free_and_null ((char **) &ub);
free_and_null ((char **) &qmatbeg);
free_and_null ((char **) &qmatcnt);
free_and_null ((char **) &qmatind);
free_and_null ((char **) &qmatval);
free_and_null ((char **) &qconrow);
free_and_null ((char **) &qconcol);
free_and_null ((char **) &qconval);
return (status);
} /* END main */
int
main (void)
{
int status, solstat;
CPXENVptr env;
CPXLPptr lp;
int i;
double x[NUMCOLS];
double cpi[NUMCOLS];
double rpi[NUMROWS];
double qpi[NUMQS];
double slack[NUMROWS], qslack[NUMQS];
double kktsum[NUMCOLS];
/* ********************************************************************** *
* *
* S E T U P P R O B L E M *
* *
* ********************************************************************** */
/* Create CPLEX environment and enable screen output.
*/
env = CPXopenCPLEX (&status);
if ( status != 0 )
goto TERMINATE;
status = CPXsetintparam (env, CPXPARAM_ScreenOutput, CPX_ON);
if ( status != 0 )
goto TERMINATE;
/* Create the problem object and populate it.
*/
lp = CPXcreateprob (env, &status, "qcpdual");
if ( status != 0 )
goto TERMINATE;
status = CPXnewcols (env, lp, NUMCOLS, obj, lb, ub, NULL, cname);
if ( status != 0 )
goto TERMINATE;
status = CPXaddrows (env, lp, 0, NUMROWS, NUMNZS, rhs, sense,
rmatbeg, rmatind, rmatval, NULL, rname);
if ( status != 0 )
goto TERMINATE;
for (i = 0; i < NUMQS; ++i) {
int const linend = (i == NUMQS - 1) ? NUMLINNZ : linbeg[i + 1];
int const quadend = (i == NUMQS - 1) ? NUMQUADNZ : quadbeg[i + 1];
status = CPXaddqconstr (env, lp, linend - linbeg[i],
quadend - quadbeg[i], qrhs[i], qsense[i],
&linind[linbeg[i]], &linval[linbeg[i]],
&quadrow[quadbeg[i]], &quadcol[quadbeg[i]],
&quadval[quadbeg[i]], qname[i]);
if ( status != 0 )
goto TERMINATE;
}
/* ********************************************************************** *
* *
* O P T I M I Z E P R O B L E M *
* *
* ********************************************************************** */
status = CPXsetdblparam (env, CPXPARAM_Barrier_QCPConvergeTol, 1e-10);
if ( status != 0 )
goto TERMINATE;
/* Solve the problem.
*/
status = CPXbaropt (env, lp);
if ( status != 0 )
goto TERMINATE;
solstat = CPXgetstat (env, lp);
if ( solstat != CPX_STAT_OPTIMAL ) {
fprintf (stderr, "No optimal solution found!\n");
goto TERMINATE;
}
/* ********************************************************************** *
* *
* Q U E R Y S O L U T I O N *
* *
* ********************************************************************** */
/* Optimal solution and slacks for linear and quadratic constraints. */
status = CPXgetx (env, lp, x, 0, NUMCOLS - 1);
if ( status != 0 )
goto TERMINATE;
status = CPXgetslack (env, lp, slack, 0, NUMROWS - 1);
if ( status != 0 )
goto TERMINATE;
status = CPXgetqconstrslack (env, lp, qslack, 0, NUMQS - 1);
if ( status != 0 )
goto TERMINATE;
/* Dual multipliers for linear constraints and bound constraints. */
status = CPXgetdj (env, lp, cpi, 0, NUMCOLS - 1);
if ( status != 0 )
goto TERMINATE;
status = CPXgetpi (env, lp, rpi, 0, NUMROWS - 1);
if ( status != 0 )
goto TERMINATE;
status = getqconstrmultipliers (env, lp, x, qpi, ZEROTOL);
if ( status != 0 )
goto TERMINATE;
/* ********************************************************************** *
* *
* C H E C K K K T C O N D I T I O N S *
* *
* Here we verify that the optimal solution computed by CPLEX (and *
* the qpi[] values computed above) satisfy the KKT conditions. *
* *
* ********************************************************************** */
/* Primal feasibility: This example is about duals so we skip this test. */
/* Dual feasibility: We must verify
* - for <= constraints (linear or quadratic) the dual
* multiplier is non-positive.
* - for >= constraints (linear or quadratic) the dual
* multiplier is non-negative.
*/
for (i = 0; i < NUMROWS; ++i) {
switch (sense[i]) {
case 'E': /* nothing */ break;
case 'R': /* nothing */ break;
case 'L':
if ( rpi[i] > ZEROTOL ) {
fprintf (stderr,
"Dual feasibility test failed for <= row %d: %f\n",
i, rpi[i]);
status = -1;
goto TERMINATE;
}
break;
case 'G':
if ( rpi[i] < -ZEROTOL ) {
fprintf (stderr,
"Dual feasibility test failed for >= row %d: %f\n",
i, rpi[i]);
status = -1;
goto TERMINATE;
}
break;
}
}
for (i = 0; i < NUMQS; ++i) {
switch (qsense[i]) {
case 'E': /* nothing */ break;
case 'L':
if ( qpi[i] > ZEROTOL ) {
fprintf (stderr,
"Dual feasibility test failed for <= quad %d: %f\n",
i, qpi[i]);
status = -1;
goto TERMINATE;
}
break;
case 'G':
if ( qpi[i] < -ZEROTOL ) {
fprintf (stderr,
"Dual feasibility test failed for >= quad %d: %f\n",
i, qpi[i]);
status = -1;
goto TERMINATE;
}
break;
}
}
/* Complementary slackness.
* For any constraint the product of primal slack and dual multiplier
* must be 0.
*/
for (i = 0; i < NUMROWS; ++i) {
if ( sense[i] != 'E' && fabs (slack[i] * rpi[i]) > ZEROTOL ) {
fprintf (stderr,
"Complementary slackness test failed for row %d: %f\n",
i, fabs (slack[i] * rpi[i]));
status = -1;
goto TERMINATE;
}
}
for (i = 0; i < NUMQS; ++i) {
if ( qsense[i] != 'E' && fabs (qslack[i] * qpi[i]) > ZEROTOL ) {
fprintf (stderr,
"Complementary slackness test failed for quad %d: %f\n",
i, fabs (qslack[i] * qpi[i]));
status = -1;
goto TERMINATE;
}
}
for (i = 0; i < NUMCOLS; ++i) {
if ( ub[i] < CPX_INFBOUND ) {
double const slk = ub[i] - x[i];
double const dual = cpi[i] < -ZEROTOL ? cpi[i] : 0.0;
if ( fabs (slk * dual) > ZEROTOL ) {
fprintf (stderr,
"Complementary slackness test failed for ub %d: %f\n",
i, fabs (slk * dual));
status = -1;
goto TERMINATE;
}
}
if ( lb[i] > -CPX_INFBOUND ) {
double const slk = x[i] - lb[i];
double const dual = cpi[i] > ZEROTOL ? cpi[i] : 0.0;
if ( fabs (slk * dual) > ZEROTOL ) {
printf ("lb=%f, x=%f, cpi=%f\n", lb[i], x[i], cpi[i]);
fprintf (stderr,
"Complementary slackness test failed for lb %d: %f\n",
i, fabs (slk * dual));
status = -1;
goto TERMINATE;
}
}
}
/* Stationarity.
* The difference between objective function and gradient at optimal
* solution multiplied by dual multipliers must be 0, i.e., for the
* optimal solution x
* 0 == c
* - sum(r in rows) r'(x)*rpi[r]
* - sum(q in quads) q'(x)*qpi[q]
* - sum(c in cols) b'(x)*cpi[c]
* where r' and q' are the derivatives of a row or quadratic constraint,
* x is the optimal solution and rpi[r] and qpi[q] are the dual
* multipliers for row r and quadratic constraint q.
* b' is the derivative of a bound constraint and cpi[c] the dual bound
* multiplier for column c.
*/
/* Objective function. */
for (i = 0; i < NUMCOLS; ++i)
kktsum[i] = obj[i];
/* Linear constraints.
* The derivative of a linear constraint ax - b (<)= 0 is just a.
*/
for (i = 0; i < NUMROWS; ++i) {
int const end = (i == NUMROWS - 1) ? NUMNZS : rmatbeg[i + 1];
int k;
for (k = rmatbeg[i]; k < end; ++k)
kktsum[rmatind[k]] -= rpi[i] * rmatval[k];
}
/* Quadratic constraints.
* The derivative of a constraint xQx + ax - b <= 0 is
* Qx + Q'x + a.
*/
for (i = 0; i < NUMQS; ++i) {
int j;
int k;
for (j = linbeg[i]; j < linbeg[i] + linnzcnt[i]; ++j)
kktsum[linind[j]] -= qpi[i] * linval[j];
for (k = quadbeg[i]; k < quadbeg[i] + quadnzcnt[i]; ++k) {
kktsum[quadrow[k]] -= qpi[i] * x[quadcol[k]] * quadval[k];
kktsum[quadcol[k]] -= qpi[i] * x[quadrow[k]] * quadval[k];
}
}
/* Bounds.
* The derivative for lower bounds is -1 and that for upper bounds
* is 1.
* CPLEX already returns dj with the appropriate sign so there is
* no need to distinguish between different bound types here.
*/
for (i = 0; i < NUMCOLS; ++i) {
kktsum[i] -= cpi[i];
}
for (i = 0; i < NUMCOLS; ++i) {
if ( fabs (kktsum[i]) > ZEROTOL ) {
fprintf (stderr, "Stationarity test failed at index %d: %f\n",
i, kktsum[i]);
status = -1;
goto TERMINATE;
}
}
/* KKT conditions satisfied. Dump out the optimal solutions and
* the dual values.
*/
printf ("Optimal solution satisfies KKT conditions.\n");
printf (" x[] =");
for (i = 0; i < NUMCOLS; ++i)
printf (" %7.3f", x[i]);
printf ("\n");
printf ("cpi[] =");
for (i = 0; i < NUMCOLS; ++i)
printf (" %7.3f", cpi[i]);
printf ("\n");
printf ("rpi[] =");
for (i = 0; i < NUMROWS; ++i)
printf (" %7.3f", rpi[i]);
printf ("\n");
printf ("qpi[] =");
for (i = 0; i < NUMQS; ++i)
printf (" %7.3f", qpi[i]);
printf ("\n");
TERMINATE:
/* ********************************************************************** *
* *
* C L E A N U P *
* *
* ********************************************************************** */
status = CPXfreeprob (env, &lp);
if ( status != 0 ) {
fprintf (stderr, "WARNING: Failed to free problem: %d\n", status);
}
status = CPXcloseCPLEX (&env);
if ( status != 0 ) {
fprintf (stderr, "WARNING: Failed to close CPLEX: %d\n", status);
}
return status;
}