An alternating direction method of multipliers with a worst-case $O(1/n^2)$ convergence rate

The Fifth Generation(5G) communication network is envisioned to provide heterogeneous services tailored to specific user demands. These services are diverse and can be generally categorized based on latency, bandwidth, reliability, and connection density requirements. The 5G infrastructure providers are expected to employ network function virtualization, software-defined networking, and network slicing for cost-effective and efficient network resource allocation. In the 5G network, when an infrastructure provider receives a slice request, a slice admission control scheme is applied and an optimization algorithm is used to achieve predefined objectives. To this end, a number of slice admission control objectives, strategies and algorithms have been proposed. However, there is a need to present a coherent review and bridge the gap between many aspects of slice admission control. In this paper, we present the latest developments in this research area. Thus, we begin by introducing slice admission control and discuss background concepts associated with slicing. We then extend our discussion to slice admission objectives followed by the strategies and optimization algorithms. Finally, we conclude with a summary of analysis containing the optimization algorithms.

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“…A typical ADMM problem with the dual update considered in Algorithm 2 has a convergence rate given by the gradient accent [41]…”

Section: B Alternating Direction Methods Of Multipliers (Admm)mentioning

confidence: 99%

A Survey on Slice Admission Control Strategies and Optimization Schemes in 5G Network

Ojijo

Falowo

2020

IEEE Access

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“…Let̃= (̃1,̃2,̃3,Λ ) be the matrix generated by PFPSM from the given and ( ,̃) be defined by (28). Then we have…”

Section: Remarkmentioning

confidence: 99%

“…For any given matrix , let̃= (̃1,̃2,̃3, Λ ) be the matrix generated by (24), ( ,̃) be defined by (28), and Θ ( ) be defined by (50). Then, one has…”

Section: Lemma 10mentioning

confidence: 99%

“…There are three strategies to deal with the issue: (1) the substitution procedure [13,21]; (2) the technique of regularization [14,22]; (3) the technique of small step size [23]. For other recent developments of ADMM, including the (sub)linear convergence rate, various acceleration techniques, indefinite regularized matrices, larger step size, and its generalization to solve nonconvex and nonsmooth multiblock separable programming, we refer to [24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

Sun

Liu

Sun

2017

Mathematical Problems in Engineering

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As a special three-block separable convex programming, the stable principal component pursuit (SPCP) arises in many different disciplines, such as statistical learning, signal processing, and web data ranking. In this paper, we propose a proximal fully parallel splitting method (PFPSM) for solving SPCP, in which the resulting subproblems all admit closed-form solutions and can be solved in distributed manners. Compared with other similar algorithms in the literature, PFPSM attaches a Glowinski relaxation factor ∈ ( √ 3/2, 2/ √ 3) to the updating formula for its Lagrange multiplier, which can be used to accelerate the convergence of the generated sequence. Under mild conditions, the global convergence of PFPSM is proved. Preliminary computational results show that the proposed algorithm works very well in practice.

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“…Additionally, their self-adaptive rule requires computing the deterministic subgradient of f (w) so that is not appropriate for stochastic optimization. Tian & Yuan [110] proposed a variant of ADMM with variable penalty parameters. Their analysis and algorithm require the smoothness assumption of ψ(Aw) and full column rank of the A matrix.…”

Section: Related Workmentioning

confidence: 99%

Accelerating convex optimization in machine learning by leveraging functional growth conditions

Xu¹

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An alternating direction method of multipliers with a worst-case $O(1/n^2)$ convergence rate

Cited by 21 publications

References 31 publications

A Survey on Slice Admission Control Strategies and Optimization Schemes in 5G Network

A Survey on Slice Admission Control Strategies and Optimization Schemes in 5G Network

A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

Accelerating convex optimization in machine learning by leveraging functional growth conditions

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