Fix the approach used to update mu (#664)

* fix mu update

* update example solutions

* remove typo

Author: nychiang

src/Drivers/MDS/NlpMdsEx1Driver.cpp

@@ -146,7 +146,7 @@ int main(int argc, char **argv)
 
 
   if(selfCheck) { // && has_empty_sp_row) {
-    if(fabs(obj_value-(-4.9994888159755632e+01))>1e-6) {
+    if(fabs(obj_value-(-4.9994906229741609e+01))>1e-6) {
       printf("selfcheck: objective mismatch for MDS Ex1 problem with 400 sparse variables and 100 "
              "dense variables did. BTW, obj=%18.12e was returned by HiOp.\n", obj_value);
       ret_code = -1;

src/Drivers/MDS/NlpMdsEx1RajaDriver.cpp

@@ -160,7 +160,7 @@ int main(int argc, char **argv)
   obj_value = solver.getObjective();
 
   if(selfCheck && has_empty_sp_row) {
-    if(fabs(obj_value-(-4.9994888159755632e+01))>1e-6) {
+    if(fabs(obj_value-(-4.9994906229741609e+01))>1e-6) {
       printf("selfcheck: objective mismatch for MDS Ex1 problem with 400 sparse variables and 100 "
              "dense variables did. BTW, obj=%18.12e was returned by HiOp.\n", obj_value);
       return -1;

src/Optimization/hiopAlgFilterIPM.cpp

@@ -547,15 +547,17 @@ bool hiopAlgFilterIPMBase::update_log_barrier_params(hiopIterate& it,
                                                      double& mu_new,
                                                      double& tau_new)
 {
-  double new_mu = fmax(eps_tol/10, fmin(kappa_mu*mu_curr, pow(mu_curr,theta_mu)));
+  const double target_comp_tol = comp_tol_/nlp->get_obj_scale();
+  double new_mu = std::fmax(0.0, std::fmin(kappa_mu*mu_curr, std::pow(mu_curr,theta_mu)));
+  new_mu = std::fmax(new_mu, std::fmin(eps_tol, target_comp_tol)/(10.+1.) );
   if(fabs(new_mu-mu_curr)<1e-16) {
     return false;
   }
   mu_new  = new_mu;
   tau_new = fmax(tau_min,1.0-mu_new);
 
   if(elastic_mode_on) {
-    const double target_mu = nlp->options->GetNumeric("tolerance");
+    const double target_mu = eps_tol;
     const double bound_relax_perturb_init = nlp->options->GetNumeric("elastic_mode_bound_relax_initial");
     const double bound_relax_perturb_min = nlp->options->GetNumeric("elastic_mode_bound_relax_final");
     double bound_relax_perturb = bound_relax_perturb_init;