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A Primal Interior Point Method for the Linear semidefinite programming problem

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2008年第10期48卷 1746-1767页

作者： Babynin, M. S. Zhadan, V. G. IV Kurchatov Atom Energy Inst Moscow 123182 Russia

The linear semidefinite programming problem is examined. A primal interior point method is proposed to solve this problem. It extends the barrier-projection method used for linear programs. The basic properties of the... 详细信息

关键词： semidefinite programming problem primal method interior point method local convergence

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Dual interior point methods for linear semidefinite programming problems

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COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS 2011年第12期51卷 2031-2051页

作者： Zhadan, V. G. Orlov, A. A. Russian Acad Sci Dorodnicyn Comp Ctr Moscow 119333 Russia

Dual interior point methods for solving linear semidefinite programming problems are proposed. These methods are an extension of dual barrier-projection methods for linear programs. It is shown that the proposed metho... 详细信息

关键词： semidefinite programming problem dual method interior point method local convergence

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A PRIMAL-DUAL INTERIOR POINT METHOD FOR PARAMETRIC semidefinite programming problemS

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Acta Mathematicae Applicatae Sinica 2000年第2期16卷 171-179页

作者：王哲民周昆平黄正海 Department of Statistics and Operations Research Fudan University Shanghai China

On the basis of primal-dual approach, we present in this paper an interior point method that gives parametric E-approximate solutions to parametric semi-definite programming problems. The method is finite, and the num... 详细信息

关键词： Interior-point method semidefinite programming problem ε-approximate solution

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Constrained Markov decision processes with uncertain costs

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OPERATIONS RESEARCH LETTERS 2022年第2期50卷 218-223页

作者： Varagapriya, V. Singh, Vikas Vikram Lisser, Abdel Indian Inst Technol Delhi Dept Math New Delhi 110016 India Univ Paris Saclay CNRS Cent Supelec Lab Signaux & Syst F-91190 Gif Sur Yvette France

We consider a finite state-action discounted constrained Markov decision process with uncertain running costs and known transition probabilities. We propose equivalent linear programming, second-order cone programming and semidefinite programming problems for the robust constrained Markov decision processes when the uncertain running cost vectors belong to polytopic, ellipsoidal, and semidefinite cone uncertainty sets, respectively. As an application, we study a variant of a machine replacement problem and perform numerical experiments on randomly generated instances of various sizes. (C) 2022 Elsevier B.V. All rights reserved.

关键词： Constrained Markov decision processes Uncertainty sets Linear programming problem Second-order cone programming problem semidefinite programming problem Machine replacement problem

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Robust set-membership filtering for systems with missing measurement: a linear matrix inequality approach

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IET SIGNAL PROCESSING 2012年第4期6卷 341-347页

作者： Yang, F. Li, Y. E China Univ Sci & Technol Sch Informat Sci & Engn Shanghai 200237 Peoples R China Cent Queensland Univ Ctr Intelligent & Networked Syst Rockhampton Qld 4702 Australia Brunel Univ Dept Informat Syst & Comp Uxbridge UB8 3PH Middx England

This study addresses the robust set-membership finite-horizon filtering problem for a class of discrete time-varying systems with missing measurement and polytopic uncertainties in the presence of unknown-but-bounded process and measurement noises. A robust set-membership filter is developed and a recursive algorithm is derived for computing the state estimate ellipsoid that is guaranteed to contain the true state. An optimal possible estimate set is computed recursively by solving the semi-definite programming problem. Simulation results are provided to demonstrate the effectiveness of the proposed method.

关键词： measurement noises linear matrix inequality approach recursive estimation Optimisation techniques state estimation missing measurement robust set-membership filtering Algebra uncertain systems state estimate ellipsoid mathematical programming optimal possible estimate set Filtering methods in signal processing linear matrix inequalities discrete time-varying systems semidefinite programming problem polytopic uncertainty robust set-membership finite-horizon filtering problem Signal processing theory discrete time systems time-varying systems recursive algorithm filtering theory unknown-but-bounded process Other topics in statistics

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Beamforming with opportunistic relaying for wireless security

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IET COMMUNICATIONS 2014年第8期8卷 1198-1210页

作者： Sarkar, Mohammad Zahurul Islam Ratnarajah, Tharmalingam Ding, Zhiguo Univ Edinburgh Sch Engn Inst Digital Commun Edinburgh EH9 3JL Midlothian Scotland Newcastle Univ Sch Elect Elect & Comp Engn Newcastle Upon Tyne NE1 7RU Tyne & Wear England

The authors present a beamforming scheme with opportunistic relaying (namely opportunistic beamforming) for wireless security under amplify-and-forward (AF) and decode-and-forward (DF) strategies. The relay selection is performed using the method of distributed timers, where all the relays use their timers to estimate own instantaneous channel gains and compete to access the wireless medium according to their own channel conditions. The performance of opportunistic beamforming scheme in terms of secure outage probability is analysed and the beamforming problem as a semidefinite programming problem with its optimisation framework is formulated. The results show that, in an opportunistic beamforming scheme, competition among cooperative relays offers diversity benefits in the direction of destination that enhances secrecy rate (i.e. minimises secure outage probability) and adhere to the opportunistic' cooperation rule giving priority to the best' available relay even when they are not chosen to transmit but rather chosen to cooperatively listen. Opportunistic beamforming scheme with DF strategy enhances secrecy rate than the beamforming with multiple DF relays while in the case of AF strategy, it provides significant improvement in the secrecy rate compared to the opportunistic relaying, the equal-power multiple-relay transmission and the single-relay transmission schemes.

关键词： cooperative communication relay networks (telecommunication) amplify and forward communication decode and forward communication probability mathematical programming array signal processing opportunistic relaying wireless security opportunistic beamforming scheme amplify-and-forward strategy decode-and-forward strategy DF strategy AF strategy secure outage probability semidefinite programming problem optimisation framework cooperative relays single-relay transmission schemes equal-power multiple-relay transmission

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Design and analysis of optimal controller for fuzzy systems with input constraint

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IEEE TRANSACTIONS ON FUZZY SYSTEMS 2004年第6期12卷 766-779页

作者： Park, Y Tahk, MJ Bang, H Korea Adv Inst Sci & Technol Dept Engn Mech Div Aerosp Engn Taejon 305701 South Korea

In this paper, we present a design method of the optimal and robust controller subject to the constraint on control inputs for continuous-time Takagi-Sugeno (TS) fuzzy systems. In order to establish this design method, we consider an optimal and robust control problem for nonlinear dynamic systems. For this problem, we present an analytic way which can provide the optimal controller for nonlinear dynamic systems by the dynamic programming approach and the inverse optimal approach. Moreover, we analyze the robustness property of the proposed optimal controller with respect to a class of input uncertainties by the passivity approach. Then, based on the theoretical results presented in this paper, we formulate the design problem of the optimal and robust. controller with input constraint for continuous-time TS fuzzy systems as the semidefinite programming, problem, and find the controller by solving it. The usefulness of the proposed approach is illustrated by considering the three-axis attitude stabilization problem of rigid spacecraft.

关键词： optimal and robust control passivity approach semidefinite programming problem spacecraft attitude control Takagi-Sugeno (TS) fuzzy system

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Beamforming strategies for multi-antenna relay-assisted networks

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IET COMMUNICATIONS 2016年第11期10卷 1384-1393页

作者： Mirzaee, Meysam Akhlaghi, Soroush Shahed Univ Dept Elect Engn Tehran Iran

Physical layer security has received considerable attentions in recent years. Moreover, cooperative communications using some nodes of network as relays make use of the benefit of multi-antenna systems such as increasing the secrecy capacity. This study studies a communication network incorporating some multi-input-multi-output amplify and forward relays in the presence of some eavesdroppers. The objective persuaded in the current work is to find the beamforming matrices at the relays to maximise the achievable secrecy rate under either individual or total power constraint at these nodes. Accordingly, three main approaches including general rank beamforming (GRBF), rank-1 beamforming (RBF) and null-space beamforming (NSBF) are developed. For the NSBF under the total power constraint, a closed-form solution is obtained, while for the remaining scenarios the corresponding optimisation problem is expressed as a semi-definite programming problem. Numerical results indicate that the RBF and NSBF methods follow GRBF in some cases and degraded from GRBF in the others. However, it is shown that these two methods have much lower complexity than GRBF.

关键词： array signal processing antenna arrays relay networks (telecommunication) telecommunication security cooperative communication MIMO communication amplify and forward communication matrix algebra mathematical programming semidefinite programming problem optimisation problem closed-form solution NSBF null-space beamforming RBF rank-1 beamforming GRBF general rank beamforming total power constraint achievable secrecy rate maximisation beamforming matrix multiinput multioutput amplify and forward relays cooperative communication physical layer security multiantenna relay-assisted network

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Hammerstein system identification using nuclear norm minimization

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AUTOMATICA 2012年第9期48卷 2189-2193页

作者： Han, Younghee de Callafon, Raymond A. Univ Calif San Diego La Jolla CA 92093 USA

This paper presents a new method for the identification of Hammerstein systems. The parameter estimation problem is formulated as a rank minimization problem by constraining a finite dimensional time dependency between signals. Due to the unknown intermediate signal, the rank minimization problem cannot be solved directly. Thus, the rank minimization problem is reformulated as an intermediate signal construction problem. The main assumption used in this paper is that static nonlinearity is monotonically non-decreasing in order to guarantee a unique combination of a static nonlinear block and a Finite Impulse Response (FIR) linear block. The rank minimization is then relaxed to a convex optimization problem using a nuclear norm. The main contribution of this paper is that the proposed method extends the rank minimization approach to Hammerstein system identification, and does not need a bilinear parametrization and singular value decomposition (SVD), which are commonly used in two-step approaches for Hammerstein system identification. (c) 2012 Elsevier Ltd. All rights reserved.

关键词： Hammerstein system identification Block-oriented system identification Rank minimization semidefinite programming problem

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Achievable secrecy rate of wiretap channels incorporating multi-input-multi-output amplify and forward relaying

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IET COMMUNICATIONS 2016年第3期10卷 300-308页

作者： Mirzaee, Meysam Akhlaghi, Soroush Shahed Univ Dept Engn Inst Modern Informat & Commun Technol Tehran Iran

This study discusses the secrecy rate of two-hop relay-assisted cooperative wiretap channels, incorporating multi-antenna amplify and forward relaying in the middle of transmission. In this regard, under the Gaussian code book assumption, three main scenarios including null-space beamforming (NSBF), rank-1 beamforming (RBF), and the so-called general rank beamforming (GRBF) are proposed to be employed at the relay where their achievable secrecy rates are studied. Accordingly, for NSBF, a closed-form solution is derived, whereas the corresponding optimisation problems are formulated for the remaining cases as a standard semi-definite programming problem. Though GRBF ranks the first in terms of the achievable secrecy rate, RBF exhibits favourable results with a much lower complexity, as the corresponding optimisation problem runs over a reduced dimension. Moreover, NSBF has a much lower complexity, as it provides an analytical solution at the expense of a decrease in the secrecy rate, and interestingly, it performs quite well when the number of eavesdroppers is less than that of the relay antennas.

关键词： relay networks (telecommunication) MIMO communication amplify and forward communication telecommunication security array signal processing antenna arrays cooperative communication Gaussian processes codes mathematical programming multiinput-multioutput amplify and forward relaying two-hop relay cooperative wiretap channels multiantenna amplify and forward relaying Gaussian code book assumption null-space beamforming NSBF rank-1 beamforming general rank beamforming GRBF semidefinite programming problem relay antennas

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