# Fixed-Time Stable Proximal Dynamical System for Solving MVIPs

arXiv: https://arxiv.org/abs/1908.03517 · HTML: https://mlsanity.com/paper/1908.03517/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2019.

## Built on by (most cited first, 4 of 4)

- [Breaking the Convergence Barrier: Optimization via Fixed-Time Convergent Flows](https://mlsanity.com/paper/2112.01363/) (2021)
- [Fixed-Time Convergence for a Class of Nonconvex-Nonconcave Min-Max Problems](https://mlsanity.com/paper/2207.12845/) (2022)
- [Generalized Gradient Flows with Provable Fixed-Time Convergence and Fast Evasion of Non-Degenerate Saddle Points](https://mlsanity.com/paper/2212.03765/) (2022)
- [From exponential to finite/fixed-time stability: Applications to optimization](https://mlsanity.com/paper/2409.11713/) (2024)

## Abstract (arXiv)

In this paper, a novel modified proximal dynamical system is proposed to compute the solution of a mixed variational inequality problem (MVIP) within a fixed time, where the time of convergence is finite and is uniformly bounded for all initial conditions. Under the assumptions of strong monotonicity and Lipschitz continuity, it is shown that a solution of the modified proximal dynamical system exists, is uniquely determined, and converges to the unique solution of the associated MVIP within a fixed time. Furthermore, the fixed-time stability of the modified projected dynamical system continues to hold, even if the assumption of strong monotonicity is relaxed to that of strong pseudomonotonicity. Finally, it is shown that the solution obtained using the forward-Euler discretization of the proposed modified proximal dynamical system converges to an arbitrarily small neighborhood of the solution of the associated MVIP within a fixed number of time steps, independent of the initial conditions.