Consistency of statistical estimators of solutions to stochastic optimization problems

Huynh Thi Hong Diem ()
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Huynh Thi Hong Diem: University of Technology

Journal of Global Optimization, 2022, vol. 83, issue 4, No 8, 825-842

Abstract: Abstract We consider the asymptotic behavior of the infimal values and the statistical estimators of the solutions to a general stochastic optimization problem. We establish the epi-convergence of the performance criteria of approximate problems when the approximate probability laws, obtained by sampling the values of the random variable, converge weakly and tightly. Based on this key convergence, consistency properties of the infimal values and the estimators of the solutions to the approximate problems are obtained. Applying these results and properties of epi/hypo-convergence of bifunctions to Lagrangians of stochastic mathematical programs, we obtain the consistency of the saddle points of approximate Lagrangians and hence the consistency of the optimal values and the estimators of the solutions of approximate mathematical programs and their dual programs.

Keywords: Stochastic optimization; Stochastic mathematical programs; Infimal values; Statistical estimators; Consistency; Weak convergence; Epi-convergence; Epi/hypo-convergence; Tightness; 90C31; 49J53; 47H04 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10898-022-01125-3

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