Linear Programming

By Julian Parsert, Cezary Kaliszyk. Arch. Formal Proofs, 2018

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The Marabou Framework for Verification and Analysis of Deep Neural Networks (2019, methodology): “It does so by implementing a variant of the simplex algorithm [3].”
Minimax Theorem for Latent Games or: How I Learned to Stop Worrying about Mixed-Nash and Love Neural Nets (2020, background): “The Nash equilibrium of a two-player zero-sum game can be cast as the solution to a linear program (Chvatal, 1983) and can thus be solved in polynomial time.”
Predictive Control for Linear and Hybrid Systems (2017, background): “Other references in this field are [217], [280] and [223, Chapter 13].”
The condition number of a function relative to a set (2019, background): “In this case it follows from [31] that the quantity 1/‖(A|X)−1‖ is precisely the distance to ill-posedness introduced by Renegar [30,31], that is, the size of the smallest perturbation ∆A on A so that the conic system (A+∆A)x = b, x ∈ X is infeasible for some b ∈ R.”
Learning to compete, coordinate, and cooperate in repeated games using reinforcement learning (2011, methodology): “…v MM i and the associated maximin strategy π MM i are given by: Since we assume that player i knows its own payoff matrix, the maximin value and strategy can be computed in polynomial time using linear programming (Chvatal 1983, Shapley 1953) , or player i ’s expected payoff when the NBS is played.”