# A sequential homotopy method for mathematical programming problems

@article{Potschka2021ASH, title={A sequential homotopy method for mathematical programming problems}, author={Andreas Potschka and Hans Georg Bock}, journal={Mathematical Programming}, year={2021}, volume={187}, pages={459-486} }

We propose a sequential homotopy method for the solution of mathematical programming problems formulated in abstract Hilbert spaces under the Guignard constraint qualification. The method is equivalent to performing projected backward Euler timestepping on a projected gradient/antigradient flow of the augmented Lagrangian. The projected backward Euler equations can be interpreted as the necessary optimality conditions of a primal-dual proximal regularization of the original problem. The…

## 4 Citations

A Preconditioned Inexact Active-Set Method for Large-Scale Nonlinear Optimal Control Problems

- Computer Science, MathematicsArXiv
- 2021

A global convergence proof of the recently proposed sequential homotopy method with an inexact Krylov–semismooth-Newton method employed as a local solver and an efficient, parallelizable, symmetric positive definite preconditioner based on a double Schur complement approach is provided.

A Flow Perspective on Nonlinear Least-Squares Problems

- Mathematics
- 2020

Just as the damped Newton method for the numerical solution of nonlinear algebraic problems can be interpreted as a forward Euler timestepping on the Newton flow equations, the damped Gauß–Newton…

A Note On Symmetric Positive Definite Preconditioners for Multiple Saddle-Point Systems

- Computer ScienceArXiv
- 2021

A preconditioner is described for multiple saddle-point systems of block tridiagonal form which can be applied within the Minres algorithm, and which has only two distinct eigenvalues, 1 and −1, when the preconditionser is applied exactly.

Constrained Structured Optimization and Augmented Lagrangian Proximal Methods

- Computer Science
- 2022

It is demonstrated how the inner subproblems can be solved by o ﬀ -the-shelf methods for composite optimization, without introducing slack variables and despite the appearance of set-valued projections.

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