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Feasible methods for nonconvex nonsmooth problems with applications in green communications

MATHEMATICAL PROGRAMMING 2017年第1-2期164卷 55-90页

作者： Facchinei, Francisco Lampariello, Lorenzo Scutari, Gesualdo Univ Roma La Sapienza Dept Comp Control & Management Engn Antonio Ruber Via Ariosto 25 I-00185 Rome Italy Univ RomaTre Dept Business Studies Via Silvio DAmico 77 I-00145 Rome Italy Purdue Univ Sch Ind Engn W Lafayette IN 47907 USA

We propose a general feasible method for nonsmooth, nonconvex constrained optimization problems. The algorithm is based on the (inexact) solution of a sequence of strongly convex optimization subproblems, followed by a step-size procedure. Key features of the scheme are: (i) it preserves feasibility of the iterates for nonconvex problems with nonconvex constraints, (ii) it can handle nonsmooth problems, and (iii) it naturally leads to parallel/distributed implementations. We illustrate the application of the method to an open problem in green communications whereby the energy consumption in MIMO multiuser interference networks is minimized, subject to nonconvex Quality-of-Service constraints.

关键词： Feasible method nonconvex problem Nonsmooth optimization Parallel and distributed implementation Green communications

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Beampattern Synthesis via First-Order Iterative Convex Approximation

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IEEE ANTENNAS AND WIRELESS PROPAGATION LETTERS 2021年第8期20卷 1493-1497页

作者： Lu, Qinghui Cui, Guolong Liu, Ruitao Yu, Xianxiang Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

This letter deals with a shaped beampattern synthesis problem through controlling the mainlobe ripple and the output filter energy based on the minimization of the peak sidelobe level in the spatial region of interest. To tackle the challenging optimization problem with nonconvex constraints, a novel first-order iterative convex approximation (FOICA) procedure that handles the nonconvex constraints with their convex upper bound functions resorting to the first-order Taylor expansion is developed. Hence, in each iteration, the original problem is approximated through a convex problem globally solved via a polynomial time method. Additionally, a nonnegative slack variable to ensure a decreasing trend in the objective function during the iteration is introduced. Finally, the numerical simulations are provided to verify that the proposed algorithm outperforms the state-of-the-art algorithms in terms of achieved beampattern performance.

关键词： Convergence Upper bound Optimization Taylor series Shape Mathematical model Linear programming Convergence first-order iterative convex approximation (FOICA) nonconvex problem phased array shaped beampattern synthesis

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Robust resource allocation for IRS-assisted secure cognitive radio networks

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ELECTRONICS LETTERS 2022年第21期58卷 816-818页

作者： Tang, Runzhe Wu, Wei Wang, Yibo Jiang, Huaixuan Nanjing Univ Posts & Telecommun Sch Commun & Informat Engn Nanjing Peoples R China Nanjing Univ Posts & Telecommun Coll Elect & Opt Engn Nanjing Peoples R China

In this paper, a robust resource allocation problem in an intelligent reflecting surface (IRS) assisted artificial noise (AN)-aided cognitive radio network is investigated. Considering that the channel state information (CSI) of the eavesdropper channel and interference channel cannot be perfectly known in practice, the aim is to minimise the power consumption of the secondary user transmitter (SU-TX) by jointly optimising the transmit beamforming and covariance matrix of AN at the SU-TX as well as the phase shifts of the IRS. The formulated problem is non-convex and challenging to tackle due to the coupling among multiple variables. An efficient alternative optimisation algorithm to solve it by exploiting the S-procedure and semi-definite relaxation. Simulation results demonstrate that the IRS helps in reducing the power consumption significantly even under imperfect CSI conditions.

关键词： covariance matrix nonconvex problem eavesdropper channel intelligent reflecting surface assisted artificial noise-aided cognitive radio network SU-TX power consumption wireless channels channel state information interference channel semidefinite programming resource allocation intelligent materials concave programming radio transmitters telecommunication power management semidefinite relaxation array signal processing alternative optimisation algorithm secondary user transmitter telecommunication security covariance matrices S-procedure IRS-assisted secure cognitive radio networks radiofrequency interference transmit beamforming IRS assisted artificial noise-aided cognitive radio network cognitive radio resource allocation problem

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Traffic Aware Resource Allocation Schemes for Multi-Cell MIMO-OFDM Systems

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2016年第11期64卷 2730-2745页

作者： Venkatraman, Ganesh Tolli, Antti Juntti, Markku Le-Nam Tran Univ Oulu Ctr Wireless Commun DCE FI-90014 Oulu Finland Maynooth Univ Dept Elect Engn Maynooth Co Kildare Ireland

We consider a downlink multi-cell multiple-input multiple-output (MIMO) interference broadcast channel (IBC) using orthogonal frequency division multiplexing (OFDM) with multiple users contending for space-frequency resources in a given scheduling instant. The problem is to design precoders efficiently to minimize the number of backlogged packets queuing in the coordinating base stations (BSs). Conventionally, the queue weighted sum rate maximization (Q-WSRM) formulation with the number of backlogged packets as the corresponding weights is used to design the precoders. In contrast, we propose joint space-frequency resource allocation (JSFRA) formulation, in which the precoders are designed jointly across the space-frequency resources for all users by minimizing the total number of backlogged packets in each transmission instant, thereby performing user scheduling implicitly. Since the problem is nonconvex, we use the combination of successive convex approximation (SCA) and alternating optimization (AO) to handle nonconvex constraints in the JSFRA formulation. In the first method, we approximate the signal-to-interference-plus-noise ratio (SINR) by convex relaxations, while in the second approach, the equivalence between the SINR and the mean squared error (MSE) is exploited. We then discuss the distributed approaches for the centralized algorithms using primal decomposition and alternating directions method of multipliers. Finally, we propose a more practical iterative precoder design by solving the Karush-Kuhn-Tucker expressions for the MSE reformulation that requires minimal information exchange for each update. Numerical results are used to compare the proposed algorithms to the existing solutions.

关键词： MIMO-IBC MIMO-OFDM precoder design SCA WSRM nonconvex problem convergence analysis

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Secure communications with untrusted relays: a multi-pair two-way relaying approach

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IET COMMUNICATIONS 2018年第20期12卷 2552-2560页

作者： Zhao, Tantan Li, Guobing Lv, Gangming Zhang, Yizhen Xi An Jiao Tong Univ Sch Elect & Informat Engn Xian 710049 Shaanxi Peoples R China China Acad Engn Phys Inst Comp Applicat Mianyang 621999 Sichuan Peoples R China ZTE Corp R& Ctr Xian Xian 710049 Shaanxi Peoples R China

Physical-layer security is usually ensured by the injection of artificial noise (AN) at the legitimate source or destination when relays are cooperative but untrusted. In this work, in order to avoid the power-consuming AN at the legitimate user pairs, the authors investigate multi-pair two-way relaying as a solution for secure transmission in wireless relay networks with untrusted relays. They formulate a generalised problem for the joint design of cooperative beamforming (CB) and AN at relays to maximise the secrecy sum-rate in wireless networks with multi-pair legal users, multiple untrusted relays as well as multiple non-colluding eavesdroppers. Further, they reformulate, approximate and relax the original non-convex problem into a sequence of convex sub-problems based on semi-definite relaxation (SDR) and Taylor series approximation. Particularly, for the reformulated problem they prove that the SDR is in fact tight, and hence propose an iterative algorithm for CB and AN design at the relays. In the simulations, they demonstrate the fast convergence and high achievable secrecy sum-rate of the proposed algorithm. Also, they simulate and discuss the impact of the number of user pairs on the secrecy sum-rate, and reveal the change of performance gain with the number of multiple user pairs.

关键词： radio networks convex programming relay networks (telecommunication) iterative methods telecommunication security concave programming cooperative communication array signal processing approximation theory multipair legal users multiple untrusted relays nonconvex problem multiple user pairs secure communications multipair two-way relaying physical-layer security legitimate source legitimate user pairs secure transmission wireless relay networks convex subproblems secrecy sum-rate maximisation artificial noise injection cooperative beamforming multiple noncolluding eavesdroppers semidefinite relaxation Taylor series approximation iterative algorithm

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Performance analysis for non-orthogonal multiple access (NOMA)-based two-way relay communication

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IET COMMUNICATIONS 2019年第4期13卷 363-370页

作者： Agarwal, Akash Jagannatham, Aditya K. Indian Inst Technol Dept Elect Engn Kanpur Uttar Pradesh India

This study analyses the performance of a non-orthogonal multiple access-based two-way relaying system. Analytical expressions are obtained to characterise the outage probability and outage floor of the system for end-to-end communication over Rayleigh fading channels. Furthermore, results are also presented for the resulting individual user and sum ergodic capacities. A user power allocation technique is proposed for sum-rate maximisation with user quality of service constraints by transforming the original non-convex problem into a difference of convex program that can be readily solved. Finally, simulation results are presented to authenticate the analytical expressions obtained for the various quantities and illustrate the efficacy of the proposed scheme.

关键词： convex programming resulting individual user sum ergodic capacities Optimisation techniques end-to-end communication relaying system analytical expressions nonorthogonal multiple access-based two-way probability fading channels optimisation simulation results nonconvex problem performance analysis study analyses outage floor user quality relay communication Rayleigh fading channels MIMO communication Radio links and equipment outage probability Rayleigh channels sum-rate maximisation radiofrequency interference user power allocation technique Other topics in statistics

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Joint source-and-relay power allocation in multiple-input multiple-output amplify-and-forward relay systems: a non-convex problem and its solution

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IET SIGNAL PROCESSING 2011年第6期5卷 612-622页

作者： Li, C. Wang, X. Yang, L. Zhu, W. -P. Southeast Univ Key Lab Underwater Acoust Signal Proc Minist Educ Sch Informat Sci & Engn Nanjing 210096 Peoples R China Nanjing Univ Dept Math Nanjing 210096 Peoples R China Concordia Univ Dept Elect & Comp Engn Montreal PQ H3G 1M8 Canada

In this study, the joint source-and-relay power allocation (JPA) problem in multiple-input multiple-output (MIMO) relay systems is investigated. It is revealed for the first time that the JPA problem based on the mean squared error (MSE) minimisation or the achievable rate maximisation criterion possesses a partial convexity, that is, the cost function is convex with respect to (w.r.t.) part of the optimisation parameters only. It is then proved that a better partial convexity, namely, a partial convexity w.r.t. a larger subset of the optimisation parameters, can be achieved by relaxing the cost function with an upper or lower bound of the MSE or achievable rate. By exploiting the partial convexity properties disclosed, two iterative algorithms are proposed to solve the non-convex JPA problem. It is shown that the convergence of the proposed iterative algorithms is guaranteed because of the fact that each iteration follows a convex optimisation w.r.t. the partial parameters. Finally, it is shown by Monte Carlo simulations that the proposed algorithms outperform several existing methods including our own prior work.

关键词： joint source-and-relay power allocation Monte Carlo simulations multiple-input multiple-output amplify-and-forward relay systems iterative methods amplify and forward communication Interpolation and function approximation (numerical analysis) iterative algorithms MIMO communication concave programming Radio links and equipment mean squared error minimisation mean square error methods Optimisation techniques Monte Carlo methods nonconvex problem cost function

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Optimal power flow algorithm and analysis in distribution system considering distributed generation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2014年第2期8卷 261-272页

作者： Sheng, Wanxing Liu, Ke-yan Cheng, Sheng China Elect Power Res Inst Power Distribut Res Dept Beijing 100192 Peoples R China

This study investigates the optimal power flow (OPF) problem for distribution networks with the integration of distributed generation (DG). By considering the objectives of minimal line loss, minimal voltage deviation and maximum DG active power output, the proposed OPF formulation is a multi-object optimisation problem. Through normalisation of each objective function, the multi-objective optimisation is transformed to single-objective optimisation. To solve such a non-convex problem, the trust-region sequential quadratic programming (TRSQP) method is proposed, which iteratively approximates the OPF by a quadratic programming with the trust-region guidance. The TRSQP utilises the sensitivity analysis to approximate all the constraints with linear ones, which will reduce the optimisation scale. Active set method is utilised in TRSQP to solve quadratic programming sub-problem. Numerical tests on IEEE 33-, PG&E 69- and actual 292-, 588-, 1180-bus systems show the applicability of the proposed method, and comparisons with the primal–dual interior point method and sequential linear programming method are provided. The initialisation and convergence condition of the proposed method are also discussed. The computational result indicates that the proposed algorithm for DG control optimisation in distribution system is feasible and effective.

关键词： DG integration sensitivity analysis PG& iterative methods linear programming actual 588-bus system Optimisation techniques E 69-bus system distributed generation actual 1180-bus system distributed power generation actual 292-bus system distribution system analysis nonconvex problem active set method minimal voltage deviation sequential linear programming method multiobject optimisation problem quadratic programming distribution networks Distribution networks Interpolation and function approximation (numerical analysis) iterative approximation Distributed power generation optimal power flow algorithm OPF problem primal-dual interior point method DG control optimisation objective function normalisation IEEE 33-bus system minimal line loss load flow trust-region sequential quadratic programming method TRSQP method maximum DG active power output single-objective optimisation

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Dislocation hyperbolic augmented Lagrangian algorithm for nonconvex optimization

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RAIRO-OPERATIONS RESEARCH 2023年第5期57卷 2941-2950页

作者： Ramirez, Lennin Mallma Maculan, Nelson Xavier, Adilson Elias Xavier, Vinicius Layter Univ Fed Rio de Janeiro Syst Engn & Comp Sci Program COPPE Rio De Janeiro Brazil Univ Fed Rio de Janeiro Syst Engn & Comp Sci Program Appl Math COPPE & IM Rio De Janeiro Brazil Univ Estado Rio De Janeiro Inst Math & Stat Grad Program Computat Sci Rio De Janeiro Brazil

The dislocation hyperbolic augmented Lagrangian algorithm (DHALA) solves the nonconvex programming problem considering an update rule for its penalty parameter and considering a condition to ensure the complementarity condition. in this work, we ensure that the sequence generated by DHALA converges to a Karush-Kuhn-Tucker (KKT) point, and we present computational experiments to demonstrate the performance of our proposed algorithm.

关键词： Dislocation hyperbolic augmented Lagrangian nonlinear programming nonconvex problem convergence complementarity condition

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Nonlinear Multivalued Periodic Systems

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JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS 2019年第2期25卷 219-243页

作者： Gasinski, Leszek Papageorgiou, Nikolaos S. Jagiellonian Univ Fac Math & Comp Sci Ul Lojasiewicza 6 PL-30348 Krakow Poland Natl Tech Univ Athens Dept Math Zografou Campus Athens 15780 Greece

We consider a first-order periodic system involving a time-dependent maximal monotone map, a subdifferential term, and a multivalued perturbation F(t, x). We prove existence theorems for the "convex" problem (that is, F is convex valued and for the "nonconvex" problem (that is, F is nonconvex valued). Also, we establish the existence of extremal trajectories (that is, solutions when the multivalued perturbation F(t, x) is replaced by ext F(t, x), the extreme points of F(t, x)). Also, we show that every solution of the convex problem can be approximated uniformly by certain extremal trajectories ("strong relaxation" theorem). Finally, we illustrate our result by examining a nonlinear periodic feedback control system.

关键词： Convex problem nonconvex problem Extremal trajectories Strong relaxation Maximal monotone map Control system

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