Tube-based robust MPC with adjustable uncertainty sets using zonotopes*

Background Antimicrobial resistance is widely considered an urgent global health issue due to associated mortality and disability, societal and healthcare costs. Aim To estimate the past, current and projected future proportion of infections resistant to treatment for eight priority antibiotic-bacterium combinations from 2000 to 2030 for 52 countries. Methods We collated data from a variety of sources including ResistanceMap and World Bank. Feature selection algorithms and multiple imputation were used to produce a complete historical dataset. Forecasts were derived from an ensemble of three models: exponential smoothing, linear regression and random forest. The latter two were informed by projections of antibiotic consumption, out-of-pocket medical spending, populations aged 64 years and older and under 15 years and real gross domestic product. We incorporated three types of uncertainty, producing 150 estimates for each country-antibiotic-bacterium-year. Results Average resistance proportions across antibiotic-bacterium combinations could grow moderately from 17% to 18% within the Organisation for Economic Co-operation and Development (OECD; growth in 64% of uncertainty sets), from 18% to 19% in the European Union/European Economic Area (EU/EEA; growth in 87% of uncertainty sets) and from 29% to 31% in Group of Twenty (G20) countries (growth in 62% of uncertainty sets) between 2015 and 2030. There is broad heterogeneity in levels and rates of change across countries and antibiotic-bacterium combinations from 2000 to 2030. Conclusion If current trends continue, resistance proportions are projected to marginally increase in the coming years. The estimates indicate there is significant heterogeneity in resistance proportions across countries and antibiotic-bacterium combinations.

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Exact recursive updating of state uncertainty sets for linear SISO systems

Automatica ◽

10.1016/j.automatica.2018.05.010 ◽

2018 ◽

Vol 95 ◽

pp. 33-43

Author(s):

Robin Hill ◽

Yousong Luo ◽

Uwe Schwerdtfeger

Keyword(s):

Uncertainty Sets ◽

State Uncertainty ◽

Recursive Updating ◽

Siso Systems

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Data Driven Robust Energy and Reserve Dispatch Based on a Nonparametric Dirichlet Process Gaussian Mixture Model

Energies ◽

10.3390/en13184642 ◽

2020 ◽

Vol 13 (18) ◽

pp. 4642

Author(s):

Li Dai ◽

Dahai You ◽

Xianggen Yin

Keyword(s):

Robust Optimization ◽

Dirichlet Process ◽

Forecast Error ◽

Optimization Methods ◽

Optimization Method ◽

Gaussian Mixture ◽

Data Driven ◽

Uncertainty Sets ◽

Uncertainty Set ◽

Simulation Results

Traditional robust optimization methods use box uncertainty sets or gamma uncertainty sets to describe wind power uncertainty. However, these uncertainty sets fail to utilize wind forecast error probability information and assume that the wind forecast error is symmetrical and independent. This assumption is not reasonable and makes the optimization results conservative. To avoid such conservative results from traditional robust optimization methods, in this paper a novel data driven optimization method based on the nonparametric Dirichlet process Gaussian mixture model (DPGMM) was proposed to solve energy and reserve dispatch problems. First, we combined the DPGMM and variation inference algorithm to extract the GMM parameter information embedded within historical data. Based on the parameter information, a data driven polyhedral uncertainty set was proposed. After constructing the uncertainty set, we solved the robust energy and reserve problem. Finally, a column and constraint generation method was employed to solve the proposed data driven optimization method. We used real historical wind power forecast error data to test the performance of the proposed uncertainty set. The simulation results indicated that the proposed uncertainty set had a smaller volume than other data driven uncertainty sets with the same predefined coverage rate. Furthermore, the simulation was carried on PJM 5-bus and IEEE-118 bus systems to test the data driven optimization method. The simulation results demonstrated that the proposed optimization method was less conservative than traditional data driven robust optimization methods and distributionally robust optimization methods.

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Trust Your Data or Not—StQP Remains StQP: Community Detection via Robust Standard Quadratic Optimization

Mathematics of Operations Research ◽

10.1287/moor.2020.1057 ◽

2020 ◽

Author(s):

Immanuel M. Bomze ◽

Michael Kahr ◽

Markus Leitner

Keyword(s):

Community Detection ◽

Optimization Problem ◽

Quadratic Optimization ◽

Quadratic Optimization Problem ◽

Standard Quadratic Optimization ◽

Uncertainty Sets ◽

Indefinite Quadratic Form ◽

Indefinite Quadratic ◽

Order Intervals ◽

Copositive Matrix

We consider the robust standard quadratic optimization problem (RStQP), in which an uncertain (possibly indefinite) quadratic form is optimized over the standard simplex. Following most approaches, we model the uncertainty sets by balls, polyhedra, or spectrahedra, more generally, by ellipsoids or order intervals intersected with subcones of the copositive matrix cone. We show that the copositive relaxation gap of the RStQP equals the minimax gap under some mild assumptions on the curvature of the aforementioned uncertainty sets and present conditions under which the RStQP reduces to the standard quadratic optimization problem. These conditions also ensure that the copositive relaxation of an RStQP is exact. The theoretical findings are accompanied by the results of computational experiments for a specific application from the domain of graph clustering, more precisely, community detection in (social) networks. The results indicate that the cardinality of communities tend to increase for ellipsoidal uncertainty sets and to decrease for spectrahedral uncertainty sets.

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