University of Connecticut

Events Calendar


Control And Optimization Seminar
Multigrid Methods For Elliptic Optimal Control Problems
Sijing Liu (University Of Connecticut)

Monday, April 12, 2021
2:00pm – 3:00pm

Other
online

Webex Meeting link: https://uconn-cmr.webex.com/uconn-cmr/j.php?MTID=m7bde33843ada4e5a3a2190673c9d4ca6

Meeting number: 120 068 6371 Password: UConn

Abstract: In this talk we present multigrid methods for linear-quadratic elliptic distributed optimal control problems.

For optimal control problems constrained by general second order elliptic partial differential equations, we design and analyze a P_1 finite element method based on a saddle point formulation. We construct a W-cycle algorithm for the discrete problem and show that it is uniformly convergent in the energy norm for convex domains. Moreover, the contraction number decays at the optimal rate of m^{-1}, where m is the number of smoothing steps. We also prove that the convergence is robust with respect to a regularization parameter. The robust convergence of V-cycle and W-cycle algorithms on general domains are demonstrated by numerical results.

For optimal control problems constrained by second order elliptic partial differential equations together with pointwise constraints on the state variable, we design and analyze symmetric positive definite P_1 finite element methods based on a reformulation of the optimal control problem as a fourth order variational inequality. We develop a multigrid algorithm for the reduced systems that appear in a primal-dual active set method for the discrete variational inequalities. The performance of the algorithm is demonstrated by numerical results.

Speaker's bio: Dr. Liu is an assistant research professor in the Department of Mathematics at the University of Connecticut.

Contact:

Bin Zou, bin.zou@uconn.edu

Control and Optimization (primary), UConn Master Calendar

Control Panel