89. Adaptivity in convex optimization beyond minimization
Invited abstract in session FB-2: First-order methods for multi-level and multi-objective optimization, stream Advances in first-order optimization.
Friday, 10:05 - 11:20Room: M:O
Authors (first author is the speaker)
| 1. | Puya Latafat
|
| Electrical Engineering (ESAT) STADIUS Center for Dynamical Systems, Signal Processing and Data Analytics, KU LEuven | |
| 2. | Andreas Themelis
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| Information Science and Electrical Engineering, Kyushu University | |
| 3. | Silvia Villa
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| Department of Mathematics, MaLGa, università di Genova | |
| 4. | Panagiotis Patrinos
|
| Electrical Engineering, KU Leuven |
Abstract
Bilevel optimization is a comprehensive framework that bridges single- and multi-objective optimization. It encompasses many general formulations, such as, but not limited to, standard nonlinear programs. This work demonstrates how elementary proximal gradient iterations can be used to solve a wide class of convex bilevel optimization problems without involving subroutines. Compared to and improving upon existing methods, ours (1) can handle a much wider class of problems, including both constraints and nonsmooth terms, (2) requires mere local Lipschitz gradient continuity of the differentiable terms without imposing any strong convexity assumptions, and (3) provides a systematic adaptive stepsize selection strategy that leads to large and nonmonotonic stepsize sequences while being insensitive to the choice of parameters.
Keywords
- Convex and non-smooth optimization
- Linear and nonlinear optimization
- Optimization for learning and data analysis
Status: accepted
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