Regularized optimization with spatial coupling for robust decision making

In high-dimensional optimization problems where a large number of decisions need to be made, the resulting solution may exhibit high sensitivity to perturbations in the input parameters, which hinders reliable decision-making. This is particularly prevalent when there is dependence between decision variables. This paper introduces a regularized optimization approach to control the trade-off between optimality and sensitivity of the solution to optimization problems that match supply and demand over a geographical area. The proposed regularization technique achieves spatial smoothing of the solution over the geographic area. It was motivated by the need of modeling intrinsic spatial dependencies between decision variables (called herein spatial coupling), thus resulting in a more realistic solution. We demonstrate the applicability of the proposed approach for multiple optimization problems. We illustrate the proposed approach using a specific application in health care access measurement, in which a smooth solution that is robust to perturbations of model parameter leads to reliable decision-making. The experimental results show that the proposed approach can be used to find a smooth and robust solution while sacrificing its optimality at a minimum level.