Journal ArticleDOI
The augmented lagrangian method for parameter estimation in elliptic systems
Kazufumi Ito,Karl Kunisch +1 more
TLDR
In this paper, a hybrid method combining the output-least-squares and the equation error method is proposed for the estimation of parameters in elliptic partial differential equations, which is realized by an augmented Lagrangian formulation, and convergence and rate of convergence proofs are provided.Abstract:
In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.read more
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Journal ArticleDOI
On optimization techniques for solving nonlinear inverse problems
TL;DR: In this article, the problem of solving nonlinear inverse problems is formulated as a constrained or unconstrained optimization problem, and by employing sparse matrix techniques, the authors show that, by formulating the inversion problem as a sequential quadratic programming (SQP) problem, they can carry out variants of SQP and the full Newton iteration with only a modest additional cost.
Journal ArticleDOI
New Proximal Point Algorithms for Convex Minimization
TL;DR: Two new proximal point algorithms for minimizing a proper, lower-semicontinuous convex function f, which converges even if f has no minimizers or is unbounded from below, are introduced.
Journal ArticleDOI
A Decomposition Methodology Applied to the Multi-Area Optimal Power Flow Problem
TL;DR: Theoretical and numerical results show that the proposed decentralized methodology has a lower computational cost than other decomposition techniques, and in large large-scale cases even lower than a centralized approach.
Journal ArticleDOI
Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
Tony F. Chan,Xue-Cheng Tai +1 more
TL;DR: In this paper, a level set approach for elliptic inverse problems with piecewise constant coefficients is proposed, where the geometry of the discontinuity of the coefficient is represented implicitly by level set functions.
Proceedings ArticleDOI
Dynamic dual decomposition for distributed control
TL;DR: It is shown how dynamic price mechanisms can be used for decomposition and distributed optimization of feedback systems, with dynamics in both decision variables and prices.