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In this paper, a joint study of the behavior of solutions of the Heavy Ball ODE and Heavy Ball type algorithms is given. Since the pioneering work of Polyak (USSR Comput Math Math Phys 4(5):1–17, 1964), it is well known that such a scheme is very efficient for C 2 strongly convex functions with Lipschitz gradient. But much less is known when only growth conditions are considered. Depending on the geometry of the function to minimize, convergence rates for convex functions, with some additional regularity such as quasi-strong convexity, or strong convexity, were recently obtained in Aujol et al. (Convergence rates of the Heavy-Ball method for quasi-strongly convex optimization, 2020). Convergence results with much weaker assumptions are given in the present paper: namely, linear convergence rates when assuming a growth condition (which amounts to a Łojasiewicz property in the convex case). This analysis is firstly performed in continuous time for the ODE, and then transposed for discrete optimization schemes. In particular, a variant of the Heavy Ball algorithm is proposed, which converges geometrically whatever the parameters choice, and which has the best state of the art convergence rate for first order methods to minimize composite non smooth convex functions satisfying a Łojasiewicz property. [ABSTRACT FROM AUTHOR]

Why did British writers, when they wrote about the Soviet Union, often deploy the imagery of numbers, arithmetic and mathematics? This paper scrutinises a number of such instances, including Orwell's famous use of the equation ‘2 + 2 = 5’ inNineteen Eighty-Fourand Koestler's fascination with Euclid's proof of the infinitude of prime numbers inThe Invisible Writing. These are put into relation with less celebrated works where questions of number or of mathematical reasoning are politicised by being applied to the Soviet Union. The paper situates these literary representations in relation to three key debates that intersected in interesting ways. Firstly, a debate about utilitarianism's attempt to quantify social goods and the Romantic rejection of that attempt; secondly, a debate about the philosophical foundations of mathematics (which involved Russell, Wittgenstein and Heidegger); and finally, a debate about the relation between mathematics and dialectical materialism, which involved key British and Soviet scientists and mathematicians and reflected on the position of science under Communism. Taking my cue from recent calls by Alain Badiou and Steven Connor for a rapprochement between the humanities and mathematics, I argue that this was a period in which numbers and arithmetic were profoundly politicised in literature. [ABSTRACT FROM PUBLISHER]