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Minimal compact operators, subdifferential of the maximum eigenvalue and semi-definite programming

LINEAR ALGEBRA AND ITS APPLICATIONS 2025年 716卷 1-31页

作者： Bottazzi, Tamara Varela, Alejandro Univ Nacl Rio Negro CITECCA Sede Andina RA-8400 San Carlos De Bariloche Argentina Consejo Nacl Invest Cient & Tecn RA-1425 Buenos Aires Argentina Inst Argentino Matemat Alberto P Calderon Saavedra 15 3er PisoC1083ACA Buenos Aires Argentina Univ Nacl Gral Sarmiento Inst Ciencias JM Gutierrez 1150B1613GSX RA-B1613GSX Los Polvorines Argentina

We formulate the issue of minimality of self-adjoint operators on a complex Hilbert space as a semi-definite problem, linking the work by Overton in [18] to the characterization of minimal hermitian matrices. This motivates us to investigate the relationship between minimal self-adjoint operators and the subdifferential of the maximum eigenvalue, initially for matrices and subsequently for compact operators. In order to do it we obtain new formulas of subdifferentials of maximum eigenvalues of compact operators that become useful in these optimization problems. Additionally, we provide formulas for the minimizing diagonals of rank one self-adjoint operators, a result that might be applied for numerical large-scale eigenvalue optimization. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Minimal operators Subdifferential of eigenvalues Moment of a subspace semi-definite programming

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semi-definite programming-based method for security-constrained unit commitment with operational and optimal power flow constraints

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IET GENERATION TRANSMISSION & DISTRIBUTION 2009年第2期3卷 182-197页

作者： Bai, X. Wei, H. Guangxi Univ Coll Elect Engn Nanning Guangxi Peoples R China

Considering the economics and securities for the operation of a power system, a semi-definite programming (SDP) model for the security-constrained unit commitment (SCUC) problem is described here, which is directly solved by the interior-point method for SDP within the polynomial times. The proposed method is promising for the SCUC problems because of its excellent convergence and the ability of handling the non-covex integer variables. No model decomposition and initial relaxation are needed when applying the SDP-based method. When the solution contains minor mismatches in the integer variables, a simple rounding strategy is used to correct the non-integer into integer efficiently. Different test cases from 6 to 118 buses over a 24 h horizon are presented. Extensive numerical simulations have shown that the proposed method is capable of obtaining the optimal UC schedules without any network and bus voltage violations, and minimising the operation cost as well.

关键词： time 24 h power system operation power system security semi-definite programming optimal power flow constraints load flow power system analysis computing interior-point method security-constrained unit commitment Power engineering computing power system economics power generation scheduling Power system management, operation and economics Optimisation techniques model decomposition dynamic programming noncovex integer variables

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semi-definite programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2009年第2期57卷 752-763页

作者： Lui, Kenneth Wing Kin Ma, Wing-Kin So, H. C. Chan, Frankie Kit Wing City Univ Hong Kong Dept Elect Engn Kowloon Hong Kong Peoples R China City Univ Hong Kong Dept Elect Engn Shatin Hong Kong Peoples R China

Finding the positions of nodes in an ad hoe wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an important and challenging research topic. However, most WSN localization studies have considered that the anchor positions and the signal propagation speed are perfectly known which is not a valid assumption in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for node localization in the presence of these uncertainties. The corresponding Cramer-Rao lower bound (CRLB) is also produced. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and CRLB.

关键词： Node localization range measurements semi-definite programming sensor networks

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semi-definite programming Approach to Stochastic Combined Heat and Power Environmental/Economic Dispatch Problem

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ELECTRIC POWER COMPONENTS AND SYSTEMS 2015年第18期43卷 2039-2049页

作者： Jubril, Abimbola Muhideen Adediji, Adeyinka Olugbenga Obafemi Awolowo Univ Dept Elect & Elect Engn Ife 220005 Nigeria

This article presents a solution to the stochastic multi-objective combined heat and power environmental/economic dispatch problem using the semi-definite programming formulation. The vector objective is reduced to an equivalent scalar objective using the weighted sum method. The resulting optimization problem is formulated as a convex optimization via semi-definite programming relaxation. The convex optimization problem was solved to obtain Pareto-optimal solutions. Improvement in the distribution of solution set was achieved through non-linear selection of the weight factor. Simulation was performed on a test problem to investigate the effectiveness of the proposed approach. Results showed that the semi-definite programming based weighted sum method has inherently good convergence property and can have its diversity property improved through weight adaptation.

关键词： cogeneration economic dispatch emission dispatch multi-objective optimization semi-definite programming weighted sum method non-linear weighted sum method combined heat and power stochastic programming

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semi-definite programming based pulse waveform design and its further analysis

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Journal of Harbin Institute of Technology(New Series) 2008年第4期15卷 578-581页

作者：王利利沙学军吴宣利 Communication Research Center Harbin Institute of Technology

In order to provide a judicious pulse waveform design required for ultra-wideband(UWB)communication to enable the UWB spectral mask compatible and coexistent with other existing wireless communication systems,a semi-definite programming(SDP)based pulse waveform design method for UWB radios is introduced and a further analysis is given in this *** using Sedumi and Yalmip toolboxes of Matlab,the procedure of solving the SDP problem is *** results show that this SDP based pulse waveform design method can be used to design pulses that fulfill the Federal Communications Commission(FCC)spectral mask strictly and optimize the power efficiency at the same *** paper also analyzes the influences of the power efficiency duing to the changes of sampling interval and the number of combined pulses,and then the optimal sampling interval that maximizes the transmission power can be found.

关键词： ultra-wideband pulse waveform design FCC spectral mask semi-definite programming

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semi-definite programming techniques for structured quadratic inverse eigenvalue problems

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NUMERICAL ALGORITHMS 2010年第4期53卷 419-437页

作者： Lin, Matthew M. Dong, Bo Chu, Moody T. N Carolina State Univ Dept Math Raleigh NC 27695 USA Dalian Univ Technol Dept Appl Math Dalian 116024 Liaoning Peoples R China

In the past decade or so, semi-definite programming (SDP) has emerged as a powerful tool capable of handling a remarkably wide range of problems. This article describes an innovative application of SDP techniques to quadratic inverse eigenvalue problems (QIEPs). The notion of QIEPs is of fundamental importance because its ultimate goal of constructing or updating a vibration system from some observed or desirable dynamical behaviors while respecting some inherent feasibility constraints well suits many engineering applications. Thus far, however, QIEPs have remained challenging both theoretically and computationally due to the great variations of structural constraints that must be addressed. Of notable interest and significance are the uniformity and the simplicity in the SDP formulation that solves effectively many otherwise very difficult QIEPs.

关键词： semi-definite programming Quadratic pencil Inverse eigenvalue problem Structural constraint Model updating

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semi-definite programming for Distributed Tracking of Dynamic Objects by Nonlinear Sensor Network

Semi-definite Programming for Distributed Tracking of Dynami...

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IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP)

作者： Rashid, U. Tuan, H. D. Kha, H. H. Nguyen, H. H. Univ New S Wales Sydney NSW Australia

ISBN: (纸本)9781457705397

This paper discusses dynamic state estimation for nonlinear measurement model through distributed multisensor network under power constraints. For this scenario, we propose an optimized power allocation strategy based on semidefinite programming, that achieves minimum mean-squared error for the estimate subject to constraints on total transmit power. System nonlinearity is handled effectively with the help of distributed unscented Kalman filtering and linear fractional transformation. Furthermore, advantage of using multiple sensors over a single independent sensor is established through simulation results for tracking a maneuvering target.

关键词： Nonlinear sensor network unscented transformation semi-definite programming distributed linear fractional transformation filtering

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semi-definite programming Based Pulse Shaping Algorithm in IEEE 802.15.4a

Semi-Definite Programming Based Pulse Shaping Algorithm in I...

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2nd International Conference on Instrumentation and Measurement, Computer, Communication and Control (IMCCC)

作者： Wu Xuan-li Sun Lu-kuan Feng Wei Luo Ming-xin Harbin Inst Technol Sch Elect & Informat Engn Harbin 150006 Peoples R China ZTE Corp Shenzhen Peoples R China

ISBN: (纸本)9780769549354

In order to increase the peak transmission data rate of Zigbee and expand its application scenario, IEEE 802.15.4a standard has been proposed in 2007, and ultra-wideband (UWB) technique has been selected as one of its physical layer standard. The performance of wireless sensor networks (WSN) will be affected by the pulse waveform transmitted in the channel, hence, in this paper, the Chinese regulation for UWB devices is firstly given, and then, a semi-definite programming based pulse shaping algorithm to comply with such regulation is proposed. Simulation results show that the proposed algorithm can comply with the given regulation with high power efficiency, which can increase the signal to noise ratio (SNR) in the receiver end.

关键词： ultra-wideband wireless sensor network pulse shaping Chinese regulation semi-definite programming

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semi-definite programming Based Waveform Design for Spectrum Sensing

Semi-Definite Programming Based Waveform Design for Spectrum...

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2nd International Conference on Frontiers of Mechanical Engineering and Materials Engineering (MEME 2013)

作者： Wu Xuan-li Sun Lu-kuan Zhao Wan-jun Harbin Inst Technol Sch Elect & Informat Engn Harbin 150006 Peoples R China

ISBN: (纸本)9783037859247

In order to solve the problem of spectrum shortages, dynamic spectrum access based cognitive radio technology was proposed, and the technology of spectrum sensing is the foundation of cognitive radio. In this paper, a semi-definite programming based waveform design algorithm is proposed for spectrum sensing. Considering the energy concentration property of Chirp signal, the Chirp signal is adopted as the basic function, which makes the composite waveform perform like impulse function in fractional Fourier transform domain. Simulation results show that the NESP (Normalized Effective Signal Power) of the designed waveform using the proposed algorithm can be over 70%, and the designed waveform also retains good energy concentration property in fractional domain.

关键词： semi-definite programming waveform design spectrum sensing cognitive radio fractional Fourier transform

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semi-definite programming APPROACH TO SENSOR NETWORK NODE LOCALIZATION WITH ANCHOR POSITION UNCERTAINTY

SEMI-DEFINITE PROGRAMMING APPROACH TO SENSOR NETWORK NODE LO...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Lui, Kenneth W. K. Ma, W-K. So, H. C. Chan, Frankie K. W. City Univ Hong Kong Dept Elect Engn Tat Chee Ave Kowloon Hong Kong Peoples R China Chinese Univ Hong Kong Dept Elect Engn Shatin Peoples R China

ISBN: (纸本)9781424423538

The problem of node localization in a wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an an important yet challenging research topic. Most WSN localization studies at present have assumed that the anchor positions are perfectly known which is not valid in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for finding the localizations of unknown-position nodes in the presence of anchor position uncertainty. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and Cramer-Rao lower bound.

关键词： sensor networks node localization range measurements semi-definite programming

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