Monotonic Optimization: Branch and Cut Methods

Tụy, Hoàng; Al-Khayyal, Faiz A.; Thach, Phan Thien

doi:10.1007/0-387-25570-2_2

Cited by 88 publications

(114 citation statements)

References 10 publications

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“…We generate the exact intracells channel as h i,i,j ∈ CN (0, I Nt ) and the uncertain intercell channels as h m,i,j ∈ CN (0, bound on the sum rate, (f min −f opt )/f opt and (f max −f opt )/f opt , respectively, for different line-search accuracies. Clearly, the proposed BRB algorithm has better convergence than the PA algorithm, which is consistent with similar observations in [2]. Note that both algorithms find quite good lower bounds after relatively few evaluations, while it takes much longer time for PA to achieve tight upper bounds than for BRB.…”

Section: Numerical Evaluation and Discussionsupporting

confidence: 85%

“…It is based on the generic BRB algorithm in [2]. Herein, we provide an outline of our multicell beamforming version, while all the details are available in [7].…”

Section: B Branch-reduce-bound (Brb) Algorithmmentioning

confidence: 99%

“…The key to solve non-convex resource allocation problems systematically is to find a suitable parameter space that represents all feasible and some infeasible strategies, and then apply some global optimization technique to iteratively reduce this space with guaranteed convergence to a global optimum [2]. Recently, other authors have proposed spaces based on beamforming parametrizations [3], power allocation [4], user rates [5], and received interference [6].…”

Section: Introductionmentioning

confidence: 99%

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Computational framework for optimal robust beamforming in coordinated multicell systems

Björnson

Bengtsson

Zheng

et al. 2011

2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

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Abstract-Coordinated beamforming can significantly improve the performance of cellular systems through joint interference management. Unfortunately, such beamforming optimization problems are typically NP-hard in multicell scenarios, making heuristic beamforming the only feasible choice in practice. This paper proposes a new branch-reduce-and-bound algorithm that solves such optimization problems globally, with a complexity suitable for benchmarking and analysis. Compared to prior work, the framework handles robustness to uncertain intercell interference and numerical analysis shows higher efficiency. I. INTRODUCTIONMost resource allocation problems in multiantenna multicell systems are non-convex and NP-hard [1], meaning that the optimal solution cannot be obtained in polynomial time. Thus, only heuristic suboptimal beamforming strategies can be applied in practice when trying to optimize, for example, the sum performance, proportional fairness, or harmonic mean. Still, it is very important to compute the optimal solution to use it as a benchmark and to study its properties.The key to solve non-convex resource allocation problems systematically is to find a suitable parameter space that represents all feasible and some infeasible strategies, and then apply some global optimization technique to iteratively reduce this space with guaranteed convergence to a global optimum In addition, all of these papers assume perfect channel state information (CSI) between all transmitters and all users in the system, which is almost impossible to achieve in practice.Herein, we propose a framework for computing optimal coordinated beamforming with robustness to CSI uncertainty. We use a new branch-reduce-and-bound (BRB) algorithm and operate in the space of the robust performance region. At each iteration, we solve a quasi-convex resource allocation problem that we call robust fairness-profile optimization (RFO). We show by simulations that the BRB algorithm is more efficient than the polyblock approximation algorithm.

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Section: Numerical Evaluation and Discussionsupporting

confidence: 85%

“…It is based on the generic BRB algorithm in [2]. Herein, we provide an outline of our multicell beamforming version, while all the details are available in [7].…”

Section: B Branch-reduce-bound (Brb) Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Computational framework for optimal robust beamforming in coordinated multicell systems

Björnson

Bengtsson

Zheng

et al. 2011

2011 4th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)

View full text Add to dashboard Cite

show abstract

“…monotonic problems: the polyblock outer approximation (PA) algorithm in [218,274] and the branch-reduce-and-bound (BRB) algorithm in [275]. These algorithms have exponential worst-case complexity, but provide a structured approach that (at least) can solve small problems.…”

Section: Example 22 (Second-order Cone Constraint)mentioning

confidence: 99%

“…There are many variations on the PA algorithm that might improve the convergence speed: (a) An improved vertex update rule is suggested in [275, Proposition 4.2] to remove more in each iteration; (b) the line-search accuracy δ can be a function of the number of iterations and the vertex g (n) [118,276]; (c) the original problem can be perturbed in an adaptive manner to further avoid shallow cuts and jamming [39,275]; (d) scheduling can be included in the algorithm [39,276]; and (e) the algorithm can be restarted from the current best solution if the number of vertices grows too large [274].…”

Section: Remark 212 (Variations)mentioning

confidence: 99%

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Björnson

Jorswieck

2012

FNT in Communications and Information Theory

149

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Deterministic Global Optimization

Pardalos

Zheng

Arulselvan

2011

Wiley Encyclopedia of Operations Research and Management Science

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Global optimization has a wide range of applications, including chemistry, engineering, biology, economics, and physics. It includes a broad range of optimization problems, where both continuous and discrete variables are involved. Unlike many optimization methods that find locally optimal solutions, global optimization methods guarantee a globally optimal solution that is intrinsically difficult to find as there might exists multiple local optima. In this survey article, we make an appraisal of the existing state of affairs in global optimization. We discuss the theoretical and algorithmic advances made in the past decades in the area of global optimization.

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Monotonic Optimization: Branch and Cut Methods

Cited by 88 publications

References 10 publications

Computational framework for optimal robust beamforming in coordinated multicell systems

Computational framework for optimal robust beamforming in coordinated multicell systems

Optimal Resource Allocation in Coordinated Multi-Cell Systems

Deterministic Global Optimization

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