virtual Real getInitialAlpha(int &ls_neval, int &ls_ngrad, const Real fval, const Real gs,
const Vector<Real> &x, const Vector<Real> &s,
Objective<Real> &obj, BoundConstraint<Real> &con) {
Real val = 1.0;
if (useralpha_) {
val = alpha0_;
}
else {
if (edesc_ == DESCENT_STEEPEST || edesc_ == DESCENT_NONLINEARCG) {
Real tol = std::sqrt(ROL_EPSILON);
Real alpha = 1.0;
// Evaluate objective at x + s
updateIterate(*d_,x,s,alpha,con);
obj.update(*d_);
Real fnew = obj.value(*d_,tol);
ls_neval++;
// Minimize quadratic interpolate to compute new alpha
alpha = -gs/(2.0*(fnew-fval-gs));
val = ((std::abs(alpha) > std::sqrt(ROL_EPSILON)) ? std::abs(alpha) : 1.0);
alpha0_ = val;
useralpha_ = true;
}
else {
val = 1.0;
}
}
return val;
}
virtual Real getInitialAlpha(int &ls_neval, int &ls_ngrad, const Real fval, const Real gs,
const Vector<Real> &x, const Vector<Real> &s,
Objective<Real> &obj, BoundConstraint<Real> &con) {
Real val = 1.0;
if (useralpha_) {
val = alpha0_;
}
else {
if (edesc_ == DESCENT_STEEPEST || edesc_ == DESCENT_NONLINEARCG) {
Real tol = std::sqrt(ROL_EPSILON);
Real alpha = 1.0;
// Evaluate objective at x + s
updateIterate(*d_,x,s,alpha,con);
obj.update(*d_);
Real fnew = obj.value(*d_,tol);
ls_neval++;
// Minimize quadratic interpolate to compute new alpha
alpha = -gs/(2.0*(fnew-fval-gs));
// Evaluate objective at x + alpha s
updateIterate(*d_,x,s,alpha,con);
obj.update(*d_);
fnew = obj.value(*d_,tol);
ls_neval++;
// Ensure that sufficient decrease and curvature conditions are satisfied
bool stat = status(LINESEARCH_BISECTION,ls_neval,ls_ngrad,alpha,fval,gs,fnew,x,s,obj,con);
if ( !stat ) {
alpha = 1.0;
}
val = alpha;
}
else {
val = 1.0;
}
}
return val;
}
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);
}
}