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

26 Pages Posted: 14 Dec 2021

See all articles by Peijun Guo

Peijun Guo

Yokohama National University - Faculty of Business Administration

Xide Zhu

School of Management, Shanghai University; School of Management, Shanghai University

Date Written: December 9, 2021

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

Suggested Citation

Guo, Peijun and Zhu, Xide and Zhu, Xide, Focus Programming Model: The Formulation of Static Stochastic Optimization Problems by Bilevel Programming Approaches (December 9, 2021). Available at SSRN: https://ssrn.com/abstract=3981460 or http://dx.doi.org/10.2139/ssrn.3981460

Peijun Guo (Contact Author)

Yokohama National University - Faculty of Business Administration ( email )

79-4 Tokiwa-dai Hodogaya-ku
Yokohama, Kanagawa, 2408501
Japan

Xide Zhu

School of Management, Shanghai University ( email )

149 Yanchang Road
SHANGDA ROAD 99
Shanghai 200444, SHANGHAI 200444
China

School of Management, Shanghai University ( email )

149 Yanchang Road
SHANGDA ROAD 99
Shanghai 200444, SHANGHAI 200444
China

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