Piecewise linear convex and concave support functions combined with Pijavskii’s method are proposed to be used for solving global optimization problems. Rules for constructing support functions are introduced.

A stability version of the Prékopa-Leindler inequality for log-concave functions on Rn is established.

Abstract Two-sided bounds are explored for concentration functions and Rényi entropies in the class of discrete log-concave probability distributions. They used to derive certain variants entropy power inequalities.

We study valid inequalities for optimizationmodels that contain both binary indicator variables and separable concave constraints. Thesemodels reduce to amixedinteger linear program (MILP) when the concave constraints are ignored, or to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms designed to solve these problems to global optimality, cutting p...

In this paper we study sparsity-inducing nonconvex penalty functions using Lévy processes. We define such a penalty as the Laplace exponent of a subordinator. Accordingly, we propose a novel approach for the construction of sparsityinducing nonconvex penalties. Particularly, we show that the nonconvex logarithmic (LOG) and exponential (EXP) penalty functions are the Laplace exponents of Gamma a...