Proximal-Point Algorithm Using a Linear Proximal Term

B. S. He (), X. L. Fu and Z. K. Jiang
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B. S. He: Nanjing University
X. L. Fu: Nanjing University
Z. K. Jiang: Nanjing University

Journal of Optimization Theory and Applications, 2009, vol. 141, issue 2, No 5, 299-319

Abstract: 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.

Keywords: Variational inequalities; Monotone variational inequalities; Proximal point algorithms; Linear proximal terms (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10957-008-9493-0

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