void compute( Vector<Real> &s, const Vector<Real> &x,
Objective<Real> &obj, BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
// Compute projected secant step
// ---> Apply inactive-inactive block of inverse secant to gradient
gp_->set(*(step_state->gradientVec));
bnd.pruneActive(*gp_,*(step_state->gradientVec),x,algo_state.gnorm);
secant_->applyH(s,*gp_);
bnd.pruneActive(s,*(step_state->gradientVec),x,algo_state.gnorm);
// ---> Add in active gradient components
gp_->set(*(step_state->gradientVec));
bnd.pruneInactive(*d_,*(step_state->gradientVec),x,algo_state.gnorm);
s.plus(gp_->dual());
s.scale(-1.0);
}
void compute( Vector<Real> &s, const Vector<Real> &x,
Objective<Real> &obj, BoundConstraint<Real> &bnd,
AlgorithmState<Real> &algo_state ) {
Real tol = std::sqrt(ROL_EPSILON<Real>());
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
// Compute projected Newton step
// ---> Apply inactive-inactive block of inverse hessian to gradient
gp_->set(*(step_state->gradientVec));
bnd.pruneActive(*gp_,*(step_state->gradientVec),x,algo_state.gnorm);
obj.invHessVec(s,*gp_,x,tol);
bnd.pruneActive(s,*(step_state->gradientVec),x,algo_state.gnorm);
// ---> Add in active gradient components
gp_->set(*(step_state->gradientVec));
bnd.pruneInactive(*d_,*(step_state->gradientVec),x,algo_state.gnorm);
s.plus(gp_->dual());
s.scale(-1.0);
}
Real GradDotStep(const Vector<Real> &g, const Vector<Real> &s,
const Vector<Real> &x,
BoundConstraint<Real> &bnd, Real eps = 0) {
Real gs(0), one(1);
if (!bnd.isActivated()) {
gs = s.dot(g.dual());
}
else {
d_->set(s);
bnd.pruneActive(*d_,g,x,eps);
gs = d_->dot(g.dual());
d_->set(x);
d_->axpy(-one,g.dual());
bnd.project(*d_);
d_->scale(-one);
d_->plus(x);
bnd.pruneInactive(*d_,g,x,eps);
gs -= d_->dot(g.dual());
}
return gs;
}
/** \brief Compute step.
Computes a trial step, \f$s_k\f$ as defined by the enum EDescent. Once the
trial step is determined, this function determines an approximate minimizer
of the 1D function \f$\phi_k(t) = f(x_k+ts_k)\f$. This approximate
minimizer must satisfy sufficient decrease and curvature conditions.
@param[out] s is the computed trial step
@param[in] x is the current iterate
@param[in] obj is the objective function
@param[in] con are the bound constraints
@param[in] algo_state contains the current state of the algorithm
*/
void compute( Vector<Real> &s, const Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &con,
AlgorithmState<Real> &algo_state ) {
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
Real tol = std::sqrt(ROL_EPSILON);
// Set active set parameter
Real eps = 0.0;
if ( con.isActivated() ) {
eps = algo_state.gnorm;
}
lineSearch_->setData(eps);
if ( hessian_ != Teuchos::null ) {
hessian_->setData(eps);
}
if ( precond_ != Teuchos::null ) {
precond_->setData(eps);
}
// Compute step s
switch(edesc_) {
case DESCENT_NEWTONKRYLOV:
flagKrylov_ = 0;
krylov_->run(s,*hessian_,*(step_state->gradientVec),*precond_,iterKrylov_,flagKrylov_);
break;
case DESCENT_NEWTON:
case DESCENT_SECANT:
hessian_->applyInverse(s,*(step_state->gradientVec),tol);
break;
case DESCENT_NONLINEARCG:
nlcg_->run(s,*(step_state->gradientVec),x,obj);
break;
case DESCENT_STEEPEST:
s.set(step_state->gradientVec->dual());
break;
default: break;
}
// Compute g.dot(s)
Real gs = 0.0;
if ( !con.isActivated() ) {
gs = -s.dot((step_state->gradientVec)->dual());
}
else {
if ( edesc_ == DESCENT_STEEPEST ) {
d_->set(x);
d_->axpy(-1.0,s);
con.project(*d_);
d_->scale(-1.0);
d_->plus(x);
//d->set(s);
//con.pruneActive(*d,s,x,eps);
//con.pruneActive(*d,*(step_state->gradientVec),x,eps);
gs = -d_->dot((step_state->gradientVec)->dual());
}
else {
d_->set(s);
con.pruneActive(*d_,*(step_state->gradientVec),x,eps);
gs = -d_->dot((step_state->gradientVec)->dual());
d_->set(x);
d_->axpy(-1.0,(step_state->gradientVec)->dual());
con.project(*d_);
d_->scale(-1.0);
d_->plus(x);
con.pruneInactive(*d_,*(step_state->gradientVec),x,eps);
gs -= d_->dot((step_state->gradientVec)->dual());
}
}
// Check if s is a descent direction i.e., g.dot(s) < 0
if ( gs >= 0.0 || (flagKrylov_ == 2 && iterKrylov_ <= 1) ) {
s.set((step_state->gradientVec)->dual());
if ( con.isActivated() ) {
d_->set(s);
con.pruneActive(*d_,s,x);
gs = -d_->dot((step_state->gradientVec)->dual());
}
else {
gs = -s.dot((step_state->gradientVec)->dual());
}
}
s.scale(-1.0);
// Perform line search
Real fnew = algo_state.value;
ls_nfval_ = 0;
ls_ngrad_ = 0;
lineSearch_->run(step_state->searchSize,fnew,ls_nfval_,ls_ngrad_,gs,s,x,obj,con);
// Make correction if maximum function evaluations reached
if(!acceptLastAlpha_)
{
lineSearch_->setMaxitUpdate(step_state->searchSize,fnew,algo_state.value);
}
algo_state.nfval += ls_nfval_;
algo_state.ngrad += ls_ngrad_;
// Compute get scaled descent direction
s.scale(step_state->searchSize);
if ( con.isActivated() ) {
s.plus(x);
con.project(s);
s.axpy(-1.0,x);
}
// Update step state information
(step_state->descentVec)->set(s);
// Update algorithm state information
algo_state.snorm = s.norm();
algo_state.value = fnew;
}
virtual bool status( const ELineSearch type, int &ls_neval, int &ls_ngrad, const Real alpha,
const Real fold, const Real sgold, const Real fnew,
const Vector<Real> &x, const Vector<Real> &s,
Objective<Real> &obj, BoundConstraint<Real> &con ) {
Real tol = std::sqrt(ROL_EPSILON);
// Check Armijo Condition
bool armijo = false;
if ( con.isActivated() ) {
Real gs = 0.0;
if ( edesc_ == DESCENT_STEEPEST ) {
updateIterate(*d_,x,s,alpha,con);
d_->scale(-1.0);
d_->plus(x);
gs = -s.dot(*d_);
}
else {
d_->set(s);
d_->scale(-1.0);
con.pruneActive(*d_,*(grad_),x,eps_);
gs = alpha*(grad_)->dot(*d_);
d_->zero();
updateIterate(*d_,x,s,alpha,con);
d_->scale(-1.0);
d_->plus(x);
con.pruneInactive(*d_,*(grad_),x,eps_);
gs += d_->dot(grad_->dual());
}
if ( fnew <= fold - c1_*gs ) {
armijo = true;
}
}
else {
if ( fnew <= fold + c1_*alpha*sgold ) {
armijo = true;
}
}
// Check Maximum Iteration
bool itcond = false;
if ( ls_neval >= maxit_ ) {
itcond = true;
}
// Check Curvature Condition
bool curvcond = false;
if ( armijo && ((type != LINESEARCH_BACKTRACKING && type != LINESEARCH_CUBICINTERP) ||
(edesc_ == DESCENT_NONLINEARCG)) ) {
if (econd_ == CURVATURECONDITION_GOLDSTEIN) {
if (fnew >= fold + (1.0-c1_)*alpha*sgold) {
curvcond = true;
}
}
else if (econd_ == CURVATURECONDITION_NULL) {
curvcond = true;
}
else {
updateIterate(*xtst_,x,s,alpha,con);
obj.update(*xtst_);
obj.gradient(*g_,*xtst_,tol);
Real sgnew = 0.0;
if ( con.isActivated() ) {
d_->set(s);
d_->scale(-alpha);
con.pruneActive(*d_,s,x);
sgnew = -d_->dot(g_->dual());
}
else {
sgnew = s.dot(g_->dual());
}
ls_ngrad++;
if ( ((econd_ == CURVATURECONDITION_WOLFE)
&& (sgnew >= c2_*sgold))
|| ((econd_ == CURVATURECONDITION_STRONGWOLFE)
&& (std::abs(sgnew) <= c2_*std::abs(sgold)))
|| ((econd_ == CURVATURECONDITION_GENERALIZEDWOLFE)
&& (c2_*sgold <= sgnew && sgnew <= -c3_*sgold))
|| ((econd_ == CURVATURECONDITION_APPROXIMATEWOLFE)
&& (c2_*sgold <= sgnew && sgnew <= (2.0*c1_ - 1.0)*sgold)) ) {
curvcond = true;
}
}
}
if (type == LINESEARCH_BACKTRACKING || type == LINESEARCH_CUBICINTERP) {
if (edesc_ == DESCENT_NONLINEARCG) {
return ((armijo && curvcond) || itcond);
}
else {
return (armijo || itcond);
}
}
else {
return ((armijo && curvcond) || itcond);
}
}
/** \brief Compute step.
Given \f$x_k\f$, this function first builds the
primal-dual active sets
\f$\mathcal{A}_k^-\f$ and \f$\mathcal{A}_k^+\f$.
Next, it uses CR to compute the inactive
components of the step by solving
\f[
\nabla^2 f(x_k)_{\mathcal{I}_k,\mathcal{I}_k}(s_k)_{\mathcal{I}_k} =
-\nabla f(x_k)_{\mathcal{I}_k}
-\nabla^2 f(x_k)_{\mathcal{I}_k,\mathcal{A}_k} (s_k)_{\mathcal{A}_k}.
\f]
Finally, it updates the active components of the
dual variables as
\f[
\lambda_{k+1} = -\nabla f(x_k)_{\mathcal{A}_k}
-(\nabla^2 f(x_k) s_k)_{\mathcal{A}_k}.
\f]
@param[out] s is the step computed via PDAS
@param[in] x is the current iterate
@param[in] obj is the objective function
@param[in] con are the bound constraints
@param[in] algo_state is the current state of the algorithm
*/
void compute( Vector<Real> &s, const Vector<Real> &x, Objective<Real> &obj, BoundConstraint<Real> &con,
AlgorithmState<Real> &algo_state ) {
Teuchos::RCP<StepState<Real> > step_state = Step<Real>::getState();
s.zero();
x0_->set(x);
res_->set(*(step_state->gradientVec));
for ( iter_ = 0; iter_ < maxit_; iter_++ ) {
/********************************************************************/
// MODIFY ITERATE VECTOR TO CHECK ACTIVE SET
/********************************************************************/
xlam_->set(*x0_); // xlam = x0
xlam_->axpy(scale_,*(lambda_)); // xlam = x0 + c*lambda
/********************************************************************/
// PROJECT x ONTO PRIMAL DUAL FEASIBLE SET
/********************************************************************/
As_->zero(); // As = 0
con.setVectorToUpperBound(*xbnd_); // xbnd = u
xbnd_->axpy(-1.0,x); // xbnd = u - x
xtmp_->set(*xbnd_); // tmp = u - x
con.pruneUpperActive(*xtmp_,*xlam_,neps_); // tmp = I(u - x)
xbnd_->axpy(-1.0,*xtmp_); // xbnd = A(u - x)
As_->plus(*xbnd_); // As += A(u - x)
con.setVectorToLowerBound(*xbnd_); // xbnd = l
xbnd_->axpy(-1.0,x); // xbnd = l - x
xtmp_->set(*xbnd_); // tmp = l - x
con.pruneLowerActive(*xtmp_,*xlam_,neps_); // tmp = I(l - x)
xbnd_->axpy(-1.0,*xtmp_); // xbnd = A(l - x)
As_->plus(*xbnd_); // As += A(l - x)
/********************************************************************/
// APPLY HESSIAN TO ACTIVE COMPONENTS OF s AND REMOVE INACTIVE
/********************************************************************/
itol_ = std::sqrt(ROL_EPSILON);
if ( useSecantHessVec_ && secant_ != Teuchos::null ) { // IHAs = H*As
secant_->applyB(*gtmp_,*As_,x);
}
else {
obj.hessVec(*gtmp_,*As_,x,itol_);
}
con.pruneActive(*gtmp_,*xlam_,neps_); // IHAs = I(H*As)
/********************************************************************/
// SEPARATE ACTIVE AND INACTIVE COMPONENTS OF THE GRADIENT
/********************************************************************/
rtmp_->set(*(step_state->gradientVec)); // Inactive components
con.pruneActive(*rtmp_,*xlam_,neps_);
Ag_->set(*(step_state->gradientVec)); // Active components
Ag_->axpy(-1.0,*rtmp_);
/********************************************************************/
// SOLVE REDUCED NEWTON SYSTEM
/********************************************************************/
rtmp_->plus(*gtmp_);
rtmp_->scale(-1.0); // rhs = -Ig - I(H*As)
s.zero();
if ( rtmp_->norm() > 0.0 ) {
//solve(s,*rtmp_,*xlam_,x,obj,con); // Call conjugate residuals
krylov_->run(s,*hessian_,*rtmp_,*precond_,iterCR_,flagCR_);
con.pruneActive(s,*xlam_,neps_); // s <- Is
}
s.plus(*As_); // s = Is + As
/********************************************************************/
// UPDATE MULTIPLIER
/********************************************************************/
if ( useSecantHessVec_ && secant_ != Teuchos::null ) {
secant_->applyB(*rtmp_,s,x);
}
else {
obj.hessVec(*rtmp_,s,x,itol_);
}
gtmp_->set(*rtmp_);
con.pruneActive(*gtmp_,*xlam_,neps_);
lambda_->set(*rtmp_);
lambda_->axpy(-1.0,*gtmp_);
lambda_->plus(*Ag_);
lambda_->scale(-1.0);
/********************************************************************/
// UPDATE STEP
/********************************************************************/
x0_->set(x);
x0_->plus(s);
res_->set(*(step_state->gradientVec));
res_->plus(*rtmp_);
// Compute criticality measure
xtmp_->set(*x0_);
xtmp_->axpy(-1.0,res_->dual());
con.project(*xtmp_);
xtmp_->axpy(-1.0,*x0_);
// std::cout << s.norm() << " "
// << tmp->norm() << " "
// << res_->norm() << " "
// << lambda_->norm() << " "
// << flagCR_ << " "
// << iterCR_ << "\n";
if ( xtmp_->norm() < gtol_*algo_state.gnorm ) {
flag_ = 0;
break;
}
if ( s.norm() < stol_*x.norm() ) {
flag_ = 2;
break;
}
}
if ( iter_ == maxit_ ) {
flag_ = 1;
}
else {
iter_++;
}
}
