# Solving generic nonarchimedean semidefinite programs using stochastic game algorithms

arXiv: https://arxiv.org/abs/1603.06916 · HTML: https://mlsanity.com/paper/1603.06916/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2016.

## Built on by (most cited first, 1 of 1)

- [On the convex formulations of robust Markov decision processes](https://mlsanity.com/paper/2209.10187/) (2022)

## Abstract (arXiv)

A general issue in computational optimization is to develop combinatorial algorithms for semidefinite programming. We address this issue when the base field is nonarchimedean. We provide a solution for a class of semidefinite feasibility problems given by generic matrices. Our approach is based on tropical geometry. It relies on tropical spectrahedra, which are defined as the images by the valuation of nonarchimedean spectrahedra. We establish a correspondence between generic tropical spectrahedra and zero-sum stochastic games with perfect information. The latter have been well studied in algorithmic game theory. This allows us to solve nonarchimedean semidefinite feasibility problems using algorithms for stochastic games. These algorithms are of a combinatorial nature and work for large instances.