Theoretical and empirical research continues on the formulation and solution of large-scale mathematical programming models and on the interpretation of results. An advanced computational test-bed enables solution of large linear, nonlinear, and mixed-integer models, as well as specialized models that invite relaxation or decomposition. Constraint and column-generation techniques are being used to solve deterministic and stochastic integer programs. Sampling-based methods are being studied for certain stochastic programs. Problems of protecting critical infrastructure, represented using bilevel and trilevel (Stackelberg game) models, defines one current focus for applications. Other applications include ship and aircraft routing, prepositioning of missile-defense assets, weapon-to-target assignment problems, and defense against bioterror. Industry and governmental agencies provide diverse applications to motivate research. Research sponsors often provide extensive staff support for important applications
References
Rockafellar RT, Royset JO: “Measures of Residual Risk with Connections to Regression, Risk Tracking, Surrogate Models, and Ambiguity.” SIAM Journal on Optimization 25(2): 117911208, 2015
Royset JO, Wets RJB: “Fusion of Hard and Soft Information in Nonparametric Density Estimation.” European Journal Operational Research 247(2): 532-547, 2015
Optimization; Stochastic programming; Optimization under uncertainty; Reliability-based optimal design; Variational analysis; Data analysis; Nonparameteric statistics; Search and detection; Risk measures;