535. An Interior-Proximal Point Method for Nonsmooth, Nonconvex PDE-Constrained Problems with State Constraints
Invited abstract in session TC-2: Infinite-dimensional optimization - Part II, stream Nonsmooth and nonconvex optimization.
Tuesday, 14:00-16:00Room: B100/7011
Authors (first author is the speaker)
| 1. | Behzad Azmi
|
| Department of Mathematics and Statistics, University of Konstantz | |
| 2. | Alberto De Marchi
|
| University of the Bundeswehr Munich |
Abstract
We consider a class of nonconvex, nonsmooth problems governed by partial differential equations (PDEs) and subject to state constraints. To address these problems, we propose a flexible algorithm that combines interior point (IP) methods with proximal gradient techniques. While traditional IP methods face difficulties with nonsmooth objective functions and proximal algorithms are typically unable to handle state constraints, their combination effectively overcomes these individual limitations. We discuss a theoretical analysis of the algorithm, including convergence and complexity results. Numerical experiments are also discussed to demonstrate the algorithm’s performance.
Keywords
- Non-smooth optimization
- First-order optimization
Status: accepted
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