Nonconvex Robust Optimization for Problems with Constraints

Authors:
Dimitris Bertsimas;Omid Nohadani;Kwong Meng Teo
Affiliations:
Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139;Operations Research Center and Sloan School of Management, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Venue:
INFORMS Journal on Computing
Year:
2010

Citing 5
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Abstract

We propose a new robust optimization method for problems with objective functions that may be computed via numerical simulations and incorporate constraints that need to be feasible under perturbations. The proposed method iteratively moves along descent directions for the robust problem with nonconvex constraints and terminates at a robust local minimum. We generalize the algorithm further to model parameter uncertainties. We demonstrate the practicability of the method in a test application on a nonconvex problem with a polynomial cost function as well as in a real-world application to the optimization problem of intensity-modulated radiation therapy for cancer treatment. The method significantly improves the robustness for both designs.