2019/04/05 by Yule Zhang, Zhang, Yule, Zehao Xiao +5
Engineering · Mathematics · #Advanced MIMO Systems Optimization #Applied mathematics #Combinatorics #Constraint (computer-aided design) #Convex optimization #Discrete mathematics #FOS: Mathematics #Geometry #Mathematical optimization #Mathematics #Multiplier (economics) #Optimization and Control (math.OC) #Order (exchange) #PAPR reduction in OFDM #Physics #Quantum mechanics #Regret #Regular polygon #Sigma #Sparse and Compressive Sensing Techniques #Statistics
paper · pdf · doi:10.48550/arxiv.1904.02862
openalex publication_date 2019/04/05 · openalex created_date 2024/02/10 · openalex updated_date 2026/07/28
In this paper, we investigate regrets of an online semi-proximal alternating direction method of multiplier (Online-spADMM) for solving online linearly constrained convex composite optimization problems. Under mild conditions, we establish \rm O(√(N)) objective regret and \rm O(√(N)) constraint violation regret at round N when the dual step-length is taken in (0,(1 +√(5))/2) and penalty parameter σ is taken as √(N). We explain that the optimal value of parameter σ is of order \rm O(√(N)). Like the semi-proximal alternating direction method of multiplier (spADMM), Online-spADMM has the advantage to resolve the potentially non-solvability issue of the subproblems efficiently. We show the usefulness of the obtained results when applied to different types of online optimization problems and verify the theoretical result by numerical experiments. The inequalities established for Online-spADMM are also used to develop iteration complexity of the average update of spADMM for solving linearly constrained convex composite optimization problems.