Work

Convex Optimal Uncertainty Quantification

Year: 2015

Type: article

Abstract: Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem, for which efficient numerical solutions can be obtained. The sufficient conditions include that the objective function is piecewise concave and the constraints are piecewise convex. In particular, we show that piecewise concave objective functions may appear in applications where the objective is defined by the optimal value of a parameterized linear program.

Source: SIAM Journal on Optimization

DOI: 10.1137/13094712x

Authors: Shuo Han, Molei Tao, Ufuk Topcu, Houman Owhadi, Richard M. Murray

Institutions: California Institute of Technology, Georgia Institute of Technology, University of Pennsylvania

Language: English

Topic: Risk and Portfolio Optimization

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funders: National Science Foundation, Air Force Office of Scientific Research

Awards: G1523888516, G4102532304, G6071252945, CPS: Small: Control Design for CyberPhysical Systems Using Slow Computing, G7830320759