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Proximal-Point Algorithm Using a Linear Proximal Term

Author

Listed:
  • B. S. He

    (Nanjing University)

  • X. L. Fu

    (Nanjing University)

  • Z. K. Jiang

    (Nanjing University)

Abstract

Proximal-point algorithms (PPAs) are classical solvers for convex optimization problems and monotone variational inequalities (VIs). The proximal term in existing PPAs usually is the gradient of a certain function. This paper presents a class of PPA-based methods for monotone VIs. For a given current point, a proximal point is obtained via solving a PPA-like subproblem whose proximal term is linear but may not be the gradient of any functions. The new iterate is updated via an additional slight calculation. Global convergence of the method is proved under the same mild assumptions as the original PPA. Finally, profiting from the less restrictions on the linear proximal terms, we propose some parallel splitting augmented Lagrangian methods for structured variational inequalities with separable operators.

Suggested Citation

  • B. S. He & X. L. Fu & Z. K. Jiang, 2009. "Proximal-Point Algorithm Using a Linear Proximal Term," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 299-319, May.
    • Handle: RePEc:spr:joptap:v:141:y:2009:i:2:d:10.1007_s10957-008-9493-0
    DOI: 10.1007/s10957-008-9493-0
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    Citations

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    Cited by:

    1. Guoyong Gu & Bingsheng He & Xiaoming Yuan, 2014. "Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach," Computational Optimization and Applications, Springer, vol. 59(1), pages 135-161, October.
    2. Zhu, Yun & Wu, Jian & Yu, Gaohang, 2015. "A fast proximal point algorithm for ℓ1-minimization problem in compressed sensing," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 777-784.

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