TY - GEN
T1 - A stochastic proximal point algorithm
T2 - 6th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
AU - Bianchi, Pascal
N1 - Publisher Copyright:
© 2016 IEEE Computer Society. All rights reserved.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Maximal monotone operators are set-valued mappings which extend (but are not limited to) the notion of subdifferential of a convex function. The proximal point algorithm is a method for finding a zero of a maximal monotone operator. The algorithm consists in fixed point iterations of a mapping called the resolvent which depends on the maximal monotone operator of interest. The paper investigates a stochastic version of the algorithm where the resolvent used at iteration k is associated to one realization of a random maximal monotone operator. We establish the almost sure ergodic convergence of the iterates to a zero of the expectation (in the Aumann sense) of the latter random operator. Application to constrained stochastic optimization is considered.
AB - Maximal monotone operators are set-valued mappings which extend (but are not limited to) the notion of subdifferential of a convex function. The proximal point algorithm is a method for finding a zero of a maximal monotone operator. The algorithm consists in fixed point iterations of a mapping called the resolvent which depends on the maximal monotone operator of interest. The paper investigates a stochastic version of the algorithm where the resolvent used at iteration k is associated to one realization of a random maximal monotone operator. We establish the almost sure ergodic convergence of the iterates to a zero of the expectation (in the Aumann sense) of the latter random operator. Application to constrained stochastic optimization is considered.
UR - https://www.scopus.com/pages/publications/85007262259
U2 - 10.1109/CAMSAP.2015.7465295
DO - 10.1109/CAMSAP.2015.7465295
M3 - Conference contribution
AN - SCOPUS:85007262259
T3 - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
BT - 2015 IEEE 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2015
PB - Institute of Electrical and Electronics Engineers Inc.
Y2 - 13 December 2015 through 16 December 2015
ER -