Optimal data fitting: a moment approach

We propose a moment relaxation for two problems, the separation and covering problem with semi-algebraic sets generated by a polynomial of degree d. We show that (a) the optimal value of the relaxation finitely converges to the optimal value of the original problem, when the moment order r increases and (b) there exist probability measures … Read more

A Data-Driven Approach to Newsvendor Problems

We propose an approach to the classical newsvendor problem and its extensions subject to uncertain demand that: (a) works directly with data, i.e., combines historical data and optimization in a single framework, (b) yields robust solutions and incorporates risk preferences using one scalar parameter, rather than utility functions, (c) allows for tractable formulations, specifically, linear … Read more

Robust and Data-Driven Optimization: Modern Decision-Making Under Uncertainty

Traditional models of decision-making under uncertainty assume perfect information, i.e., accurate values for the system parameters and specific probability distributions for the random variables. However, such precise knowledge is rarely available in practice, and a strategy based on erroneous inputs might be infeasible or exhibit poor performance when implemented. The purpose of this tutorial is … Read more