Expected Residual Minimization Formulation for Stochastic Absolute Value Equations

Jingyong Tang () and Jinchuan Zhou ()
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Jingyong Tang: Xinyang Normal University
Jinchuan Zhou: Shandong University of Technology

Journal of Optimization Theory and Applications, 2024, vol. 203, issue 1, No 24, 675 pages

Abstract: Abstract In this paper we investigate a class of stochastic absolute value equations (SAVE). After establishing the relationship between the stochastic linear complementarity problem and SAVE, we study the expected residual minimization (ERM) formulation for SAVE and its Monte Carlo sample average approximation. In particular, we show that the ERM problem and its sample average approximation have optimal solutions under the condition of $$R_0$$ R 0 pair, and the optimal value of the sample average approximation has uniform exponential convergence. Furthermore, we prove that the solutions to the ERM problem are robust for SAVE. For a class of SAVE problems, we use its special structure to construct a smooth residual and further study the convergence of the stationary points. Finally, a smoothing gradient method is proposed by simultaneously considering sample sampling and smooth techniques for solving SAVE. Numerical experiments exhibit the effectiveness of the method.

Keywords: Stochastic absolute value equations; Expected residual minimization formulation; Monte Carlo approximation; Smoothing gradient method (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-024-02527-x

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