  


Distributionally robust optimization with polynomial densities: theory, models and algorithms
Etienne de Klerk(E.deKlerkuvt.nl) Abstract: In distributionally robust optimization the probability distribution of the uncertain problem parameters is itself uncertain, and a fictitious adversary, e.g., nature, chooses the worst distribution from within a known ambiguity set. A common shortcoming of most existing distributionally robust optimization models is that their ambiguity sets contain pathological discrete distribution that give nature too much freedom to in ict damage. We thus introduce a new class of ambiguity sets that contain only distributions with sumofsquares polynomial density functions of known degrees. We show that these ambiguity sets are highly expressive as they conveniently accommodate distributional information about higherorder moments, conditional probabilities, conditional moments or marginal distributions. Exploiting the theoretical properties of a measurebased hierarchy for polynomial optimization due to Lasserre [SIAM J. Optim. 21(3) (2011), pp. 864885], we prove that certain worstcase expectation constraints are computationally tractable under these new ambiguity sets. We showcase the practical applicability of the proposed approach in the context of a stylized portfolio optimization problem and a risk aggregation problem of an insurance company. Keywords: distributionally robust optimization, semidefinite programming, sumofsquares polynomials, generalized eigenvalue problem Category 1: Robust Optimization Category 2: Linear, Cone and Semidefinite Programming (Semidefinite Programming ) Citation: Download: [PDF] Entry Submitted: 05/09/2018 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  