265. Progressive decoupling of linkage problems beyond elicitable monotonicity
Invited abstract in session FC-2: Algorithms for Variational inequalities and equilibria, stream Advances in first-order optimization.
Friday, 11:25 - 12:40Room: M:O
Authors (first author is the speaker)
| 1. | Brecht Evens
|
| Department of Electrical Engineering ESAT-STADIUS, KU Leuven | |
| 2. | Puya Latafat
|
| Electrical Engineering (ESAT) STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU LEuven | |
| 3. | Panagiotis Patrinos
|
| Electrical Engineering, KU Leuven |
Abstract
In this talk, we study the progressive decoupling algorithm and Spingarn's method of partial inverses for finding a point in the graph of an operator such that the first, primal variable belongs to a closed subspace and the second, dual variable belongs to its orthogonal complement. This so-called linkage problem encompasses many problems emerging in optimization and variational inequalities, owing to its close connection with Lagrangian duality. In particular, we establish convergence of both methods in the absense of any (elicitable) monotonicity assumptions, by leveraging their connection with the preconditioned proximal point method. Additionally, we showcase the broad range of problems our theory is able to cover through several illustrative examples.
Keywords
- Complementarity and variational problems
Status: accepted
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