Use of nondifferentiable optimization in a health care problem

Those who study health care systems (HSC) seek to model the features of health care systems of societies that are common to different countries, so as to assist those who plan health services. The mathematicians interested in nondifferentiable optimization (NDO) seek to extend the classical optimization techniques to functions that have "non-smooth" regions where no unique gradient can be defined. This article reports how a health resource allocation model was solved by minimizing a function with points of nondifferentiability. It describes how an example of the model arose in the joint strategic planning of health and personal social services in a county in England with a population of about one million. It also formulates the model as a problem of NDO. Ways to obtain numerical solutions are reviewed, and the solution of the example by NDO is compared to another method based on linear approximation.