Journal
IEEE TRANSACTIONS ON SIGNAL PROCESSING
Volume 66, Issue 22, Pages 5941-5955Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2018.2871389
Keywords
Two-stage non-convex stochastic optimization; successive convex approximation; online optimization
Categories
Funding
- Science and Technology Program of Shenzhen, China [JCYJ20170818113908577]
- National Natural Science Foundation of China [61571383]
- RGC [16209916]
- China Recruitment Program of Global Young Experts
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Two-stage stochastic optimization, in which a long-term master problem is coupled with a family of short-term subproblems, plays a critical role in various application areas. However, most existing algorithms for two-stage stochastic optimization only work for special cases, and/or are based on the batch method, which requires huge memory and computational complexity. To the best of our knowledge, there still lack efficient and general two-stage online stochastic optimization algorithms. This paper proposes a two-stage online successive convex approximation (TOSCA) algorithm for general two-stage nonconvex stochastic optimization problems. At each iteration, the TOSCA algorithm first solves one short-term subproblem associated with the current realization of the system state. Then, it constructs a convex surrogate function for the objective of the long-term master problem. Finally, the long-term variables are updated by solving a convex approximation problem obtained by replacing the objective function in the long-term master problem with the convex surrogate function. We establish the almost sure convergence of the TOSCA algorithm and customize the algorithmic framework to solve three important application problems. Simulations show that the TOSCA algorithm can achieve superior performance over existing solutions.
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