double GradientProjection::computeSteepestDescentVector(
valarray<double> const &b,
valarray<double> const &x,
valarray<double> &g) const {
// find steepest descent direction
// g = 2 ( b - A x )
// where: A = denseQ + sparseQ
// g = 2 ( b - denseQ x) - 2 sparseQ x
//
// except the 2s don't matter because we compute
// the optimal stepsize anyway
COLA_ASSERT(x.size()==b.size() && b.size()==g.size());
g = b;
for (unsigned i=0; i<denseSize; i++) {
for (unsigned j=0; j<denseSize; j++) {
g[i] -= (*denseQ)[i*denseSize+j]*x[j];
}
}
// sparse part:
if(sparseQ) {
valarray<double> r(x.size());
sparseQ->rightMultiply(x,r);
g-=r;
}
return computeStepSize(g,g);
}
LOCA::Abstract::Iterator::StepStatus
LOCA::Stepper::preprocess(LOCA::Abstract::Iterator::StepStatus stepStatus)
{
if (stepStatus == LOCA::Abstract::Iterator::Unsuccessful) {
// Restore previous step information
curGroupPtr->copy(*prevGroupPtr);
}
else {
// Save previous successful step information
prevGroupPtr->copy(*curGroupPtr);
}
// Compute step size
stepStatus = computeStepSize(stepStatus, stepSize);
// Set step size in current solution group
curGroupPtr->setStepSize(stepSize);
// Set previous solution vector in current solution group
curGroupPtr->setPrevX(prevGroupPtr->getX());
// Take step in predictor direction
curGroupPtr->computeX(*prevGroupPtr, *curPredictorPtr, stepSize);
// Allow continuation group to preprocess the step
curGroupPtr->preProcessContinuationStep(stepStatus);
// Reset solver to compute new solution
solverPtr = NOX::Solver::buildSolver(curGroupPtr, noxStatusTestPtr,
parsedParams->getSublist("NOX"));
return stepStatus;
}
/*
* Use gradient-projection to solve an instance of
* the Variable Placement with Separation Constraints problem.
*/
unsigned GradientProjection::solve(
valarray<double> const &linearCoefficients,
valarray<double> &x) {
COLA_ASSERT(linearCoefficients.size()==x.size());
COLA_ASSERT(x.size()==denseSize);
COLA_ASSERT(numStaticVars>=denseSize);
COLA_ASSERT(sparseQ==nullptr ||
(sparseQ!=nullptr && (vars.size()==sparseQ->rowSize())) );
if(max_iterations==0) return 0;
bool converged=false;
solver = setupVPSC();
#ifdef MOSEK_AVAILABLE
if(solveWithMosek==Outer) {
float* ba=new float[vars.size()];
float* xa=new float[vars.size()];
for(unsigned i=0;i<vars.size();i++) {
ba[i]=-linearCoefficients[i];
}
mosek_quad_solve_sep(menv,ba,xa);
for(unsigned i=0;i<vars.size();i++) {
//printf("mosek result x[%d]=%f\n",i,xa[i]);
x[i]=xa[i];
}
delete [] ba;
delete [] xa;
return 1;
}
#endif
// it may be that we have to consider dummy vars, which the caller didn't know
// about. Thus vars.size() may not equal x.size()
unsigned n = vars.size();
valarray<double> b(n);
result.resize(n);
// load desired positions into vars, note that we keep desired positions
// already calculated for dummy vars
for (unsigned i=0;i<x.size();i++) {
COLA_ASSERT(!isNaN(x[i]));
COLA_ASSERT(isFinite(x[i]));
b[i]=i<linearCoefficients.size()?linearCoefficients[i]:0;
result[i]=x[i];
if(scaling) {
b[i]*=vars[i]->scale;
result[i]/=vars[i]->scale;
}
if(!vars[i]->fixedDesiredPosition) vars[i]->desiredPosition=result[i];
}
runSolver(result);
valarray<double> g(n); /* gradient */
valarray<double> previous(n); /* stored positions */
valarray<double> d(n); /* actual descent vector */
#ifdef CHECK_CONVERGENCE_BY_COST
double previousCost = DBL_MAX;
#endif
unsigned counter=0;
double stepSize;
for (; counter<max_iterations&&!converged; counter++) {
previous=result;
stepSize=0;
double alpha=computeSteepestDescentVector(b,result,g);
//printf("Iteration[%d]\n",counter);
// move to new unconstrained position
for (unsigned i=0; i<n; i++) {
// dividing by variable weight is a cheap trick to make these
// weights mean something in terms of the descent vector
double step=alpha*g[i]/vars[i]->weight;
result[i]+=step;
//printf(" after unconstrained step: x[%d]=%f\n",i,result[i]);
stepSize+=step*step;
COLA_ASSERT(!isNaN(result[i]));
COLA_ASSERT(isFinite(result[i]));
if(!vars[i]->fixedDesiredPosition) vars[i]->desiredPosition=result[i];
}
//project to constraint boundary
bool constrainedOptimum = false;
constrainedOptimum=runSolver(result);
stepSize=0;
for (unsigned i=0;i<n;i++) {
double step = previous[i]-result[i];
stepSize+=step*step;
}
//constrainedOptimum=false;
// beta seems, more often than not, to be >1!
if(constrainedOptimum) {
// The following step limits the step-size in the feasible
// direction
d = result - previous;
const double beta = 0.5*computeStepSize(g, d);
// beta > 1.0 takes us back outside the feasible region
// beta < 0 clearly not useful and may happen due to numerical imp.
//printf("beta=%f\n",beta);
if(beta>0&&beta<0.99999) {
stepSize=0;
for (unsigned i=0; i<n; i++) {
double step=beta*d[i];
result[i]=previous[i]+step;
stepSize+=step*step;
}
}
}
#ifdef CHECK_CONVERGENCE_BY_COST
/* This would be the slow way to detect convergence */
//if(counter%2) {
double cost = computeCost(b,result);
printf(" gp[%d] %.15f %.15f\n",counter,previousCost,cost);
//COLA_ASSERT(previousCost>cost);
if(fabs(previousCost - cost) < tolerance) {
converged = true;
}
previousCost = cost;
//}
#else
if(stepSize<tolerance) converged = true;
#endif
}
//printf("GP[%d] converged after %d iterations.\n",k,counter);
for(unsigned i=0;i<x.size();i++) {
x[i]=result[i];
if(scaling) {
x[i]*=vars[i]->scale;
}
}
destroyVPSC(solver);
return counter;
}
