The Discrete Moment Problem with Nonconvex Shape Constraints

The discrete moment problem aims to find a worst-case distribution that satisfies given set of moments. This paper studies the problems with additional shape constraints guarantee is either log-concave (LC) or has an increasing failure rate (IFR) generalized (IGFR). These classes are useful in practice, applications revenue management, reliability, and inventory control. authors characterize structure optimal extreme point distributions show, for example, solution m moments LC piecewise geometric at most pieces. Using this optimality structure, they design exact algorithm computing solutions low-dimensional space parameters. leverage study robust newsvendor compute solutions.