250. On a Unified Analysis of Kernel-based Interior Point Algorithms
Invited abstract in session FB-6: Higher-order Methods in Mathematical Programming II, stream Challenges in nonlinear programming.
Friday, 10:05 - 11:20Room: M:H
Authors (first author is the speaker)
| 1. | Marianna E.-Nagy
|
| Corvinus University of Budapest | |
| 2. | Zsolt Darvay
|
| Department of Mathematics and Computer Science of the Hungarian Line, Babes-Bolyai University | |
| 3. | Goran Lesaja
|
| Mathematical Sciences, Georgia Southern University | |
| 4. | Petra Renáta Rigó
|
| Corvinus University of Budapest | |
| 5. | Anita Varga
|
| Corvinus Centre for Operations Research, Corvinus University of Budapest |
Abstract
Kernel-based interior point algorithms (IPA) were developed to improve the theoretical complexity of large step IPAs. In the literature, various kernel functions were defined and an upper bound was given on the iteration number of the corresponding IPAs. In 2010, Lesaja and Roos considered eligible kernel function based IPAs for sufficient linear complementarity problems and provided a general scheme for steps of the complexity analysis. However, this framework necessitates independently verifying its steps for different kernel functions.
To address this challenge, we propose additional, not very restrictive conditions on the class of eligible kernel functions and present a unified analysis for these kernel-based IPAs. Our subset of eligible kernel functions contains all kernel functions with polynomial and exponential barrier terms mentioned in the literature. We demonstrate consistent complexity bounds across all cases.
Keywords
- Linear and nonlinear optimization
- SS - Conic Optimization and Applications
Status: accepted
Back to the list of papers