===affil2:
George Mason University
===firstname:
Zichao
===firstname4:

===firstname3:
Stephen
===lastname2:
Emelianenko
===lastname:
Di
===firstname5:

===affil6:

===lastname3:
Nash
===email:
zdi@masonlive.gmu.edu
===lastname6:

===affil5:

===otherauths:

===lastname4:

===affil4:

===lastname7:

===affil7:

===firstname7:

===postal:
5541 Ridgeton Hill Ct. Fairfax, VA, 22032
===firstname6:

===ABSTRACT:
This talk will present recent progress related to the theory and applications of the multilevel optimization approach MG/OPT. Inspired by the traditional multigrid, the intent of MG/OPT is to use calculations on coarser levels to accelerate the progress of the optimization on the finest level. There are several advantages of MG/OPT: first of all, the optimization perspective is broader than systems of equations since it can handle the constraints in a more natural way. Also, MG/OPT has stronger guarantees of convergence than traditional multigrid. Furthermore, in many cases the reduced Hessian of the optimization model is an elliptic operator making MG/OPT an effective algorithm. 
So far, MG/OPT has been successfully applied to many PDE-constrained optimization problems which have regular geometric structures. However, in practice, more sophisticated implementations that provide an easier way to apply MG/OPT to specific problems are still under exploration.
In order to investigate the potential of MG/OPT to solve the problems with irregular geometric structures, MG/OPT is applied to a particular type of tessellation problems called centroidal Voronoi tessellations(CVTs). Significant speedup by using MG/OPT comparing to other existing techniques has shown. 

Furthermore, the constrained version of MG/OPT has also been developed and it has been applied to successfully solve a variety of other constrained optimization problems.
===affil3:
George Mason University
===lastname5:

===affilother:

===title:
Applications and Recent Developments of Multilevel Optimization Framework(MG/OPT)
===firstname2:
Maria