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Exact penalty and error bounds in DC programming

JOURNAL OF GLOBAL OPTIMIZATION 2012年第3期52卷 509-535页

作者： Hoai An Le Thi Tao Pham Dinh Huynh Van Ngai Univ Paul Verlaine Metz UFR MIM Lab Theoret & Appl Comp Sci LITA EA 3097 F-57045 Metz France LMI Natl Inst Appl Sci Rouen F-76801 St Etienne France Univ Quynhon Dept Math Qui Nhon Vietnam

In the present paper, we are concerned with conditions ensuring the exact penalty for nonconvex programming. Firstly, we consider problems with concave objective and constraints. Secondly, we establish various results on error bounds for systems of DC inequalities and exact penalty, with/without error bounds, in DC programming. They permit to recast several class of difficult nonconvex programs into suitable DC programs to be tackled by the efficient DCA.

关键词： DC programming concave programming DCA Subdifferential Exact penalty Local and global error bounds Reformulation

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Efficient transceiver beamforming in multiple-input-multiple-output cognitive radio network

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IET COMMUNICATIONS 2014年第15期8卷 2729-2736页

作者： Zhu, Fangjun Guo, Yan Li, Ning PLA Univ Sci & Technol Coll Commun Engn Nanjing 210007 Jiangsu Peoples R China

Owing to the ability of improving spectrum utilisation and quality-of-service (QoS) in wireless communications, multiple-input-multiple-output (MIMO) cognitive radio (CR) network has been identified as an excellent choice for the next generation communication. To protect primary users (PUs) from excessive interference while ensuring a meaningful QoS of secondary users (SUs), one key challenge of such system is the joint design of transceiver beamforming for SUs. In this study, the authors investigate the beamforming in MIMO CR network, and two optimisation problems in terms of the minimisation of the total transmission power and the maximisation of the smallest received signal-to-interference-plus-noise ratio (SINR) are considered. The problems can be formulated as indefinite quadratic optimisation programs which are known to be non-convex NP-hard. Hence, a distributed algorithm based on semi-definite programming and minimum-mean-squared-error is proposed to achieve the optimal beamforming weight vector. The findings of this study demonstrated that the proposed algorithm outperforms the existing ones with respect to the total transmitted power and SUs SINR.

关键词： radio transceivers array signal processing MIMO communication cognitive radio quality of service minimisation computational complexity distributed algorithms least mean squares methods concave programming radio spectrum management radiofrequency interference quadratic programming multiple-input-multiple-output cognitive radio network spectrum utilisation quality-of-service QoS wireless communication MIMO CR network next generation communication primary user protection excessive interference secondary user transceiver beamforming efficiency optimisation problem total transmission power minimisation signal-to-interference-plus-noise ratio SINR maximisation indefinite quadratic optimisation program nonconvex NP-hard distributed algorithm semidefinite programming minimum-mean-squared-error optimal beamforming weight vector

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Computing the controllability radius: a semi-definite programming approach

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IET CONTROL THEORY AND APPLICATIONS 2009年第6期3卷 654-660页

作者： Dumitrescu, B. Sicleru, B. C. Stefan, R. Univ Politehn Bucuresti Dept Automat Control & Comp Bucharest 060042 Romania Tampere Univ Technol Tampere Int Ctr Signal Proc FIN-33101 Tampere Finland

A semi-definite programming (SDP) approach to compute the controllability radius is proposed in this paper. The initial nonconvex optimisation problem is transformed into the minimisation of the smallest eigenvalue of a bivariate real or trigonometric polynomial with matrix coefficients. A sum-of-squares relaxation leads to the SDP formulation. A similar technique is used for the computation of the stabilisability radius. The approach is extended to the computation of the worst-case controllability radius for systems that depend polynomially on a small number of parameters. Experimental results show that the proposed methods compete well with previous ones in a complexity/accuracy trade-off.

关键词： worst-case controllability radius Optimisation techniques eigenvalues and eigenfunctions controllability stability trigonometric polynomial Stability in control theory Linear algebra (numerical analysis) sum-of-square relaxation smallest bivariate real eigenvalue minimisation stabilisability radius concave programming matrix coefficient semidefinite programming nonconvex optimisation problem polynomial matrices

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On optimum multi-input multi-output radar signal design: Ambiguity function, manifold structure and duration-bandwidth

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IET SIGNAL PROCESSING 2021年第1期15卷 46-60页

作者： Liu, Yuqing Xu, Jia Wong, Kon Max Davidson, Timothy N. Zhengzhou Univ Sch Informat Engn Zhengzhou Peoples R China McMaster Univ Dept ECE Hamilton ON Canada

A design technique is developed for the probing signals of a Multi-Input Multi-Output (MIMO) radar. The concentration of the energy of the signal in its essential duration and essential bandwidth is achieved through the use of a class of time-frequency concentrated functions called the WLJ functions as the synthesizing signal set. The goal is to design a signal vector having a pre-specified desired covariance (CoV) matrix while ensuring that the side-lobes of the ambiguity functions are small. Since CoV matrices are structurally constrained, they form a manifold in the signal space. Hence, we argue that the difference between these matrices should not be measured in terms of the conventional Euclidean distance (ED);rather, the distance should be measured along the surface of the manifold, that is, in terms of a Riemannian distance (RD). In either case, the signal optimisation problem is non-convex in the design variables, involving, respectively, a quartic and a square-root objective function. An efficient algorithm based on successive convex approximation is developed in which the original non-convex problems are transformed so that they can be approximated by a convex quadratically constrained quadratic problem at each stage, resulting in good approximate solutions. Comparing the designs using ED and RD, we find that the convergence of the algorithm can be significantly faster when optimising over the manifold (RD) than when optimising over the whole space (ED). More importantly, for tight constraints, the use of RD yields solutions which satisfy the constraints far better than the use of ED.

关键词： approximation theory concave programming convex programming covariance matrices iterative methods matrix algebra mean square error methods MIMO communication optimisation quadratic programming radar signal processing set theory statistical analysis MIMO radar

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Optimal synthesis of reconfigurable sparse arrays via multi-convex programming

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IET RADAR SONAR AND NAVIGATION 2020年第8期14卷 1125-1134页

作者： Qi, Zhengdong Bai, Yechao Wang, Qiong Zhang, Xinggan Chen, Hao Nanjing Univ Sch Elect Sci & Engn Nanjing 210023 Peoples R China CSIC 724 Res Inst Nanjing Peoples R China Anhui Normal Univ Sch Phys & Elect Informat Wuhu 241002 Peoples R China

A new approach for the synthesis of one-dimensional (1D) and 2D reconfigurable sparse arrays generating sum and difference power patterns is presented in this study. In the case of 1D arrays, the design procedure provides solutions in which only one set of amplitude coefficients is required and the reconfigurability is obtained by modifying only the excitation phases. In the case of 2D arrays, the simplification of the antenna system is investigated by sharing some excitations for the sum and difference channels. An iterative scheme is used where the array response in the main lobe direction is cast as a multi-convex problem at each step that the non-convex lower bound constraint is relaxed while concurrently minimising a reweighted objective function based on the magnitudes of the element excitations. To ensure the robustness of the array, worst-case performance optimisation technique and white noise gain constraint are introduced in the array. Numerical tests and electromagnetic simulations, referred to known optimal solutions, show that the proposed design is able to obtain good radiation performance with a smaller number of elements.

关键词： iterative methods convex programming antenna radiation patterns antenna arrays white noise concave programming minimisation electromagnetic simulations numerical testing white noise gain constraint reweighted objective function minimisation iterative scheme antenna system 1D reconfigurable sparse array synthesis 2D reconfigurable sparse array synthesis performance optimisation technique nonconvex lower bound constraint multiconvex programming

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Hybrid precoding for millimetre wave MIMO systems based on particle swarm optimisation

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IET COMMUNICATIONS 2019年第11期13卷 1643-1650页

作者： Cui, Mingyang Zou, Weixia Wang, Ye Zhang, Ran Beijing Univ Posts & Telecommun MOE Key Lab Univ Wireless Commun Beijing 100876 Peoples R China Southeast Univ State Key Lab Millimeter Waves Nanjing 210096 Jiangsu Peoples R China

Millimetre wave (mmWave) multiple-input multiple-output (MIMO) systems have been proposed to enable Gbps communication for next-generation cellular systems and local area networks. To compensate for the severe propagation loss of the mmWave channel, a cost-effective hybrid precoding architecture, combining a digital precoder and an analogue precoder, is widely used in mmWave MIMO systems. In this study, two hybrid precoding algorithms based on particle swarm optimisation (PSO) algorithm will be proposed for two different hybrid precoding structures, i.e. the fully connected and partially connected structures. First, the authors use the phase of the analogue precoding variable to replace the corresponding variable with the constraints of the unit norm to solve the non-convex constraints skillfully. Then they design analogue precoding by using PSO algorithm and compute the digital precoding based on the least squares solution. Finally, the proposed algorithms are compared with the existing advanced algorithms. Simulation results demonstrate that the proposed algorithms can approach the optimal performance under the corresponding structure.

关键词： particle swarm optimisation precoding MIMO communication channel coding concave programming millimetre wave communication cellular radio local area networks wireless channels digital precoder analogue precoder mmWave MIMO systems hybrid precoding algorithms particle swarm optimisation algorithm fully connected structures partially connected structures analogue precoding PSO algorithm digital precoding millimetre wave MIMO systems millimetre wave multiple-input multiple-output systems next-generation cellular systems local area networks severe propagation loss mmWave channel cost-effective hybrid precoding architecture hybrid precoding structures least squares solution nonconvex constraints

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RIS-Aided Zero-Forcing and Regularized Zero-Forcing Beamforming in Integrated Information and Energy Delivery

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2022年第7期21卷 5500-5513页

作者： Yu, Hongwen Hoang Duong Tuan Dutkiewicz, Eryk Poor, H. Vincent Hanzo, Lajos Univ Technol Sydney Sch Elect & Data Engn Broadway Campus Ultimo NSW 2007 Australia Princeton Univ Dept Elect & Comp Engn Princeton NJ 08544 USA Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England

This paper considers a network of a multi-antenna array base station (BS) and a reconfigurable intelligent surface (RIS) to deliver both information to information users (IUs) and power to energy users (EUs). The RIS links the connection between the IUs and the BS as there is no direct path between the former and the latter. The EUs are located nearby the BS in order to effectively harvest energy from the high-power signal from the BS, while the much weaker signal reflected from the RIS hardly contributes to the EUs' harvested energy. To provide reliable links for all users over the same time-slot, we adopt the transmit time-switching (transmit-TS) approach, under which information and energy are delivered over different time-slot fractions. This allows us to rely on conjugate beamforming for energy links and zero-forcing/regularized zero-forcing beamforming (ZFB/RZFB) and on the programmable reflecting coefficients (PRCs) of the RIS for information links. We show that ZFB/RZFB and PRCs can be still separately optimized in their joint design, where PRC optimization is based on iterative closed-form expressions. We then develop a path-following algorithm for solving the max-min IU throughput optimization problem subject to a realistic constraint on the quality-of-energy-service in terms of the EUs' harvested energy thresholds. We also propose a new RZFB for substantially improving the IUs' throughput.

关键词： Optimization Throughput Array signal processing Resource management Wireless communication Fading channels Symmetric matrices Reconfigurable intelligent surface transmit beamforming conjugate beamforming zero-forcing beamforming trigonometric function optimization concave programming

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Pareto-optimal radar waveform design

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IET RADAR SONAR AND NAVIGATION 2011年第4期5卷 473-482页

作者： De Maio, A. Piezzo, M. Farina, A. Wicks, M. Univ Naples Federico II Dipartimento Ingn Biomed Elettron & Telecomunicaz I-80125 Naples Italy SELEX Sistemi Integrati I-00131 Rome Italy US AFRL Sensors Directorate Rome NY 13441 USA

This study deals with the problem of Pareto-optimal waveform design in the presence of coloured Gaussian noise, under a similarity and an energy constraint. At the design stage, the authors, determine the optimal radar code according the following criterion: constrained maximisation of the detection performance and constrained minimisation of the Cramer-Rao lower bound (CRLB) on the Doppler estimation accuracy. This is tantamount to jointly maximising two quadratic forms under two quadratic constraints, so that the problem can be formulated in terms of a non-convex multi-objective optimisation problem. In order to solve it, the authors resort to the scalarisation technique, which reduces the vectorial problem into a scalar one using a Pareto weight defining the relative importance of the two objective functions. At the analysis stage, the authors assess the performance of the proposed waveform design scheme in terms of detection performance, region of achievable Doppler estimation accuracy and ambiguity function. In particular, the authors analyse the role of the Pareto weight in the optimisation process.

关键词： radar signal processing Pareto-optimal radar waveform design quadratic constraint Cramer-Rao lower bound scalarisation technique concave programming ambiguity function Gaussian noise Other topics in statistics nonconvex multi-objective optimisation problem Optimisation techniques Radar equipment, systems and applications Doppler estimation accuracy Signal processing and detection CRLB coloured Gaussian noise

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Delay aware scheduling in UAV-enabled OFDMA mobile edge computing system

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IET COMMUNICATIONS 2020年第18期14卷 3203-3211页

作者： Liu, Siyang Yang, Tingting Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200240 Peoples R China Dongguan Univ Technol Sch Elect Engn & Intelligentizat Dongguan 523000 Peoples R China Peng Cheng Lab Shenzhen 518000 Peoples R China

In infrastructure-less scenarios such as rural environments, wild emergency response, military applications and disaster relief, unmanned aerial vehicles (UAVs) are capable of providing enhanced mobile edge computing (MEC) services for ground users. Although small latency is the most important advantage of MEC system, how to provide delay aware scheduling in UAV-enabled MEC system still remains unsolved. In this study, the authors investigate the delay aware scheduling problem in UAV-enabled orthogonal frequency division multiple access (OFDMA) MEC system and formulate two non-convex optimisation problems. Moreover, they consider uplink and downlink architecture with characteristics in different UAV-ground links and traffic load. Furthermore, they propose two novel multi-stages resource allocation algorithms, i.e. the JSPA-T and JSPA-F algorithms with respect to downlink transmit power allocation and sub-carrier assignment. The mathematical frameworks with duality theory based alternative search optimisation and successive approximation method are proposed. The simulation results validate the performance improvement of the proposed solutions as well as the fast converge behaviour and small computational complexity.

关键词： quality of service computational complexity radio networks resource allocation OFDM modulation frequency division multiple access autonomous aerial vehicles mobile computing telecommunication scheduling search problems approximation theory concave programming UAV-enabled OFDMA mobile edge computing system infrastructure-less scenarios rural environments wild emergency response military applications disaster relief unmanned aerial vehicles enhanced mobile edge computing services ground users UAV-enabled MEC system delay aware scheduling problem UAV-enabled orthogonal frequency division multiple access MEC system nonconvex optimisation problems uplink architecture downlink architecture UAV-ground links multistages resource allocation algorithms downlink transmit power allocation computational complexity

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Hybrid algorithm for dynamic economic dispatch with valve-point effects

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IET GENERATION TRANSMISSION & DISTRIBUTION 2013年第10期7卷 1096-1104页

作者： Chen, Yan Wen, Jinyu Jiang, Lin Cheng, Shijie Huazhong Univ Sci & Technol State Key Lab Adv Electromagnet Engn & Technol Wuhan 430074 Peoples R China Univ Liverpool Dept Elect Engn & Elect Liverpool L69 3GJ Merseyside England

Dynamic economic dispatch problem in power system considering valve-point effects of generators is a non-smooth, non-convex and multi-dimensional constrained optimisation problem. In allusion to those characteristics, this study proposes a hybrid algorithm which integrates low-discrepancy sequences, improved shuffled frog leaping algorithm and sequential quadratic programming. The effectiveness of the proposed method has been verified by using case studies based on 5-unit, 10-unit and 30-unit test systems over a period of 24 h. The results show that the proposed method has improved solution quality and computation efficiency, compared with most current approaches.

关键词： concave programming power generation dispatch power generation economics quadratic programming time 24 h test systems sequential quadratic programming improved shuffled frog leaping algorithm low-discrepancy sequences nonsmooth optimisation problem nonconvex optimisation problem multidimensional constrained optimisation problem generators power system dynamic economic dispatch problem valve-point effects hybrid algorithm

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