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Stability Analysis of Stochastic Generalized Equation via Brouwer’s Fixed Point Theorem

Author

Listed:
  • Qiang Liu
  • Jie Zhang
  • Shuang Lin
  • Li-wei Zhang

Abstract

The stochastic generalized equation provides a unifying methodology to study several important stochastic programming problems in engineering and economics. Under some metric regularity conditions, the quantitative stability analysis of solutions of a stochastic generalized equation with the variation of the probability measure is investigated via Brouwer’s fixed point theorem. In particular, the error bounds described by Hausdorff distance between the solution sets are established against the variation of the probability measure. The stability results obtained are finally applied to a stochastic conic programming.

Suggested Citation

  • Qiang Liu & Jie Zhang & Shuang Lin & Li-wei Zhang, 2018. "Stability Analysis of Stochastic Generalized Equation via Brouwer’s Fixed Point Theorem," Mathematical Problems in Engineering, Hindawi, vol. 2018, pages 1-8, March.
    • Handle: RePEc:hin:jnlmpe:8680540
    DOI: 10.1155/2018/8680540
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