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This is a classic question in the literature on linear programming, since it is related to the stability of the feasible set (and hence the solutions) under perturbation of the parameters. The classic work in this field is: A. J. Hoffman, Approximate solutions of systems of linear inequalities, J. Res. Nat. Bur. Standards, 1952. A more recent work, which ...

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A curvature bound for a non-smooth metric space is often known as a "synthetic curvature bound" or a "coarse curvature." Here's one possible definition for the concept. Definition: A condition $Q_{\kappa}$ is a synthetic lower bound for a curvature tensor $R$ if the following two conditions hold: (1) On a smooth manifold $M$ where $R$ is ...

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