Semi-smooth Newton Methods for Non-differentiable Optimization Problems Lipschitz Lectures

2 These notes constitute no original research work. Rather they draw from the results with collaborators that are quoted in the reference section.

[1]  J. C. de los Reyesa,et al.  A semi-smooth Newton method for control constrained boundary optimal control of the Navier–Stokes equations , 2005 .

[2]  Hyung-Chun Lee,et al.  Analysis and Computational Methods of Dirichlet Boundary Optimal Control Problems for 2D Boussinesq Equations , 2003, Adv. Comput. Math..

[3]  Karl Kunisch,et al.  Trading Regions Under Proportional Transaction Costs , 2006, OR.

[4]  Karl Kunisch,et al.  Path-following Methods for a Class of Constrained Minimization Problems in Function Space , 2006, SIAM J. Optim..

[5]  Karl Kunisch,et al.  Optimal Vortex Reduction for Instationary Flows Based on Translation Invariant Cost Functionals , 2007, SIAM J. Control. Optim..

[6]  Karl Kunisch,et al.  Total Bounded Variation Regularization as a Bilaterally Constrained Optimization Problem , 2004, SIAM J. Appl. Math..

[7]  H. Soner,et al.  Optimal Investment and Consumption with Transaction Costs , 1994 .

[8]  Kazufumi Ito,et al.  The Primal-Dual Active Set Method for Nonlinear Optimal Control Problems with Bilateral Constraints , 2004, SIAM J. Control. Optim..

[9]  Boris Vexler,et al.  Adaptivity with Dynamic Meshes for Space-Time Finite Element Discretizations of Parabolic Equations , 2007, SIAM J. Sci. Comput..

[10]  Kazufumi Ito,et al.  Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces , 2000 .

[11]  Karl Kunisch,et al.  A semi-smooth Newton method for solving elliptic equations with gradient constraints , 2009 .

[12]  Angela Kunoth,et al.  Adaptive wavelet schemes for an elliptic control problem with Dirichlet boundary control , 2005, Numerical Algorithms.

[13]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[14]  K. Kunisch,et al.  An active set strategy based on the augmented Lagrangian formulation for image restoration , 1999 .

[15]  I. Ekeland,et al.  Convex analysis and variational problems , 1976 .

[16]  E. Giusti Minimal surfaces and functions of bounded variation , 1977 .

[17]  Roland Becker,et al.  Mesh adaptation for Dirichlet flow control via Nitsche's method , 2002 .

[18]  Kazufumi Ito,et al.  The Primal-Dual Active Set Strategy as a Semismooth Newton Method , 2002, SIAM J. Optim..

[19]  L. Hou,et al.  Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with Dirichlet controls , 1991 .

[20]  Karl Kunisch,et al.  Feasible and Noninterior Path-Following in Constrained Minimization with Low Multiplier Regularity , 2006, SIAM J. Control. Optim..