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Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem

Author

Listed:
  • Wenli Liu
  • Xiaoni Chi
  • Qili Yang
  • Ranran Cui

Abstract

In this paper, a weighted second-order cone (SOC) complementarity function and its smoothing function are presented. Then, we derive the computable formula for the Jacobian of the smoothing function and show its Jacobian consistency. Also, we estimate the distance between the subgradient of the weighted SOC complementarity function and the gradient of its smoothing function. These results will be critical to achieve the rapid convergence of smoothing methods for weighted SOC complementarity problems.

Suggested Citation

  • Wenli Liu & Xiaoni Chi & Qili Yang & Ranran Cui, 2021. "Jacobian Consistency of a Smoothing Function for the Weighted Second-Order Cone Complementarity Problem," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-11, January.
    • Handle: RePEc:hin:jnlmpe:6674520
    DOI: 10.1155/2021/6674520
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