A Cutting-Plane Global Optimization Algorithm for a Special Non-Convex Problem

This study establishes the convergence of a cutting-plane algorithm tailored for a specific non-convex optimization problem. The presentation begins with the problem definition, accompanied by the necessary hypotheses that substantiate the application of a cutting plane. Following this, we develop an algorithm designed to tackle the problem. Lastly, we provide a demonstration that the sequence … Read more

Data-driven distributionally robust optimization: Intersecting ambiguity sets, performance analysis and tractability

We consider stochastic programs in which the probability distribution of uncertain parameters is unknown and partial information about it can only be captured from limited data. We use distributionally robust optimization (DRO) to model such problems. As opposed to the commonly used approach for DRO problems that suggests creating an ambiguity set by following a specific … Read more

Cutting-plane algorithm for sparse estimation of the Cox proportional-hazards model

Survival analysis is a family of statistical methods for analyzing event occurrence times. In this paper, we address the mixed-integer optimization approach to sparse estimation of the Cox proportional-hazards model for survival analysis. Specifically, we propose a high-performance cutting-plane algorithm based on reformulation of bilevel optimization for sparse estimation. This algorithm solves the upper-level problem … Read more