Quasi-Newton approaches to interior point methods for quadratic problems

Gondzio, Jacek; Sobral, F. N. C.

doi:10.1007/s10589-019-00102-z

“…This kind of problems are solved by interior point methods with computational complexity O(M 3 ), assuming that the matrix structure is not exploited. However, the efficiency is improvable by exploiting channel sparsity [27], or by using Quasy-Newtown methods [28]. In addition, the convergence rate is specially fast: O( √ M ).…”

Section: Regardless Of the Group Of Users Inh (N)mentioning

confidence: 99%

Power Efficient Scheduling and Hybrid Precoding for Time Modulated Arrays

González-Coma

¹

,

Castedo

²

2020

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We consider power efficient scheduling and precoding solutions for multiantenna hybrid digital-analog transmission systems that use Time-Modulated Arrays (TMAs) in the analog domain. TMAs perform beamforming with switches instead of conventional Phase Shifters (PSs). The extremely low insertion losses of switches, together with their reduced power consumption and cost make TMAs attractive in emerging technologies like massive Multiple-Input Multiple-Output (MIMO) and millimeter wave (mmWave) systems. We propose a novel analog processing network based on TMAs and provide an angular scheduling algorithm that overcomes the limitations of conventional approaches. Next, we pose a convex optimization problem to determine the analog precoder. This formulation allows us to account for the Sideband Radiation (SR) effect inherent to TMAs, and achieve remarkable power efficiencies with a very low impact on performance. Computer experiments results show that the proposed design, while presenting a significantly better power efficiency, achieves a throughput similar to that obtained with other strategies based on angular selection for conventional architectures. INDEX TERMS Time modulated array, hybrid precoding, massive MIMO, mmWave, user scheduling.

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“…This kind of problems are solved by interior point methods with computational complexity O(M 3 ), assuming that the matrix structure is not exploited. However, the efficiency is improvable by exploting channel sparsity [27], or by using Quasy-Newtown methods [28]. In addition, the convergence rate is specially fast: O( √ M ).…”

Section: A Computing Desired Precoding Directionsmentioning

confidence: 99%

“…Hybrid Precoding 1: R (0) ← 0, n ← 1 Update using(28) and Θ (n) Update with(29) and Θ (n) (n) ← Update with S (n)11: P (n) ← Normalization and Waterfilling 12:…”

mentioning

confidence: 99%

Power Efficient Scheduling and Hybrid Precoding for Time Modulated Arrays

González-Coma¹,

Castedo²

2019

Preprint

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We consider power efficient scheduling and precoding solutions for multiantenna hybrid digital-analog transmission systems that use Time-Modulated Arrays (TMAs) in the analog domain. TMAs perform beamforming with switches instead of conventional Phase Shifters (PSs). The extremely low insertion losses of switches, together with their reduced power consumption and cost make TMAs attractive in emerging technologies like massive Multiple-Input Multiple-Output (MIMO) and millimeter wave (mmWave) systems. We propose a novel analog processing network based on TMAs and provide an angular scheduling algorithm that overcomes the limitations of conventional approaches. Next, we pose a convex optimization problem to determine the analog precoder. This formulation allows us to account for the Sideband Radiation (SR) effect inherent to TMAs, and achieve remarkable power efficiencies with a very low impact on performance. Computer experiments results show that the proposed design, while presenting a significantly better power efficiency, achieves a throughput similar to that obtained with other strategies based on angular selection for conventional architectures.<br>

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“…[13,29,30]) and in particular on the effect that an inexact linear solver has on the convergence properties of IPMs ( [6,11,24,28]). Many other improvements have been made regarding predictor-correctors strategies [12,21], regularization strategies [3,19,36] or the use of quasi-Newton approaches [14,15,26].…”

Section: Introductionmentioning

confidence: 99%

A new stopping criterion for Krylov solvers applied in Interior Point Methods

Zanetti¹,

Gondzio²

2021

Preprint

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A surprising result is presented in this paper with possible far reaching consequences for any optimization technique which relies on Krylov subspace methods employed to solve the underlying linear equation systems. In this paper the advantages of the new technique are illustrated in the context of Interior Point Methods (IPMs). When an iterative method is applied to solve the linear equation system in IPMs, the attention is usually placed on accelerating their convergence by designing appropriate preconditioners, but the linear solver is applied as a black box solver with a standard termination criterion which asks for a sufficient reduction of the residual in the linear system. Such an approach often leads to an unnecessary "oversolving" of linear equations. In this paper a new specialized termination criterion for Krylov methods used in IPMs is designed. It is derived from a deep understanding of IPM needs and is demonstrated to preserve the polynomial worst-case complexity of these methods. The new criterion has been adapted to the Conjugate Gradient (CG) and to the Minimum Residual method (MINRES) applied in the IPM context. The new criterion has been tested on a set of linear and quadratic optimization problems including compressed sensing, image processing and instances with partial differential equation constraints. Evidence gathered from these computational experiments shows that the new technique delivers significant improvements in terms of inner (linear) iterations and those translate into significant savings of the IPM solution time.

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Quasi-Newton approaches to interior point methods for quadratic problems

Cited by 15 publications

References 30 publications

Power Efficient Scheduling and Hybrid Precoding for Time Modulated Arrays

Power Efficient Scheduling and Hybrid Precoding for Time Modulated Arrays

Power Efficient Scheduling and Hybrid Precoding for Time Modulated Arrays

A new stopping criterion for Krylov solvers applied in Interior Point Methods

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