Focus Programming: A Fundamental Alternative for Stochastic Optimization Problems

A fundamental alternative for stochastic optimization problems named focus programming is proposed based on the focus theory of choice. Different from the existing approaches such as chance-constrained programming and two-stage stochastic programming which are based on expected utility theory, focus programming determines the optimal solution according to which solution’s focus (the most salient realization of random vector) is the most preferred. Focus programming models are bilevel programming problems with maximin-type upper and lower level programs which are interesting and challenging. Two equivalent single-level reformulations of the focus programming models have been proposed for the discrete random vector case.