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Focus programming: a bi-level programming approach to static stochastic optimization problems
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DOI：10.1111/itor.13322.png)
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Abstract
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Static stochastic optimization problems are formulated with the focus theory of choice where 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 is a bi-level programming approach 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-level 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 bi-level programming problems. We propose several single-level reformulation methods for such problems.
Keywords:
nonlinear programming
bi-level programming
focus theory of choice
static stochastic optimization problem
mathematical program with vanishing
equilibrium constraints
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AMERICAN ECONOMIC REVIEW
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AMERICAN ECONOMIC REVIEWIF11.6
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