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Bilevel Optimization of the Kantorovich Problem and its Quadratic Regularization Part II: Convergence Analysis
Sebastian Hillbrecht, Paul Manns, Christian Meyer
This paper is concerned with an optimization problem that is constrained by the Kantorovich optimal transportation problem. This bilevel optimization problem can be reformulated as…
-Regularization of the Beckmann Problem
Dirk Lorenz, Hinrich Mahler, Christian Meyer
We investigate the problem of optimal transport in the so-called Beckmann form, i.e. given two Radon measures on a compact set, we seek an optimal flow field which is a vector valu…
Optimal Control of Perfect Plasticity Part II: Displacement Tracking
Christian Meyer, Stephan Walther
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement…
Optimal Control of Perfect Plasticity Part I: Stress Tracking
Christian Meyer, Stephan Walther
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress fi…
Quadratically regularized optimal transport
Dirk A. Lorenz, Paul Manns, Christian Meyer
We investigate the problem of optimal transport in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, we seek an optimal transport plan which is ano…
A non-smooth trust-region method for locally Lipschitz functions with application to optimization problems constrained by variational inequalities
Constantin Christof, Juan Carlos De Los Reyes, Christian Meyer
We propose a nonsmooth trust-region method for solving optimization problems with locally Lipschitz continuous functions, with application to problems constrained by variational in…