Focus Programming Model: The Formulation of Static Stochastic Optimization Problems by Bilevel Programming Approaches

Abstract

Static stochastic optimization problems are formulated with the focus theory of choice
in which instead of using the expected utility in the existing approaches, the optimal solution is
determined as per which solution’s focus (the most salient realization of a random vector) is the most
preferred. The new formulation that we call the focus programming model is a bilevel programming
problem in which the lower level program is used to choose the focus of each feasible solution and the
upper level program is to determine the optimal solution. Since in focus programming models upper
and lower level programs are maximin or minimax problems, they are nonsmooth and sometimes even
nonconvex so that the existing optimization methods cannot solve such bilevel programming problems.
We propose several tractable single-level reformulation methods for such challenging problems.

Keywords: nonlinear programming, bilevel programming, focus theory of choice, stochastic programming problem

JEL Classification: C02