An Inertial Accelerated Predictor–Corrector Algorithm for Exponential Variational Inequalities with Sharp Convergence Guarantees and Applications
Abstract
We study exponentially convex nonlinearities and exponentially monotone operators in Hilbert spaces for exponential variational inequalities (EVIs). We show that the exponential nonlinearity is the gradient of a convex functional, so it is monotone. We use this fact to prove existence, uniqueness, and contractivity of the associated fixed-point mapping for every strong monotonicity constant α>0 of the underlying operator. This task is performed using an explicit, computable step-size range and linear convergence rate. We present a two-step inertial predictor–corrector technique and prove its strong convergence. Applying the framework to the Bratu obstacle problem (which models thermal ignition in combustion systems) yields the explicit, sharp requirement (b−a)2eM
Fields of Study & Subjects
Optimization and Variational Analysis
Contact Mechanics and Variational Inequalities
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- Algorithms
- Publisher
- MDPI AG
- Volume
- 19
- Issue
- 8
- Pages
- 647–647
- Publication date
- 5 August 2026
- Language
- EN