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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Y. Sun P. Babu D. P. Palomar Dept. of Electron. & Comput. Eng. Hong Kong Univ. of Sci. & Technol. Hong Kong China

ISBN: (纸本)9781467369985

In this paper, we consider the robust covariance estimation problem in the non-Gaussian set-up. In particular, Tyler's M-estimator is adopted for samples drawn from a heavy-tailed elliptical distribution. For some applications, the covariance matrix naturally possesses certain structure. Therefore, incorporating the prior structure information in the estimation procedure is beneficial to improving estimation accuracy. The problem is formulated as a constrained minimization of the Tyler's cost function, where the structure is characterized by the constraint set. A numerical algorithm based on majorization-minimization is derived for general structures that can be characterized as a convex set, where a sequence of convex programming is solved. For the set of matrices that can be decomposed as the sum of rank one positive semidefinite matrices, which has a wide range of applications, the algorithm is modified with much lower complexity. Simulation results demonstrate that the proposed structure-constrained Tyler's estimator achieves smaller estimation error than the unconstrained case.

关键词： Robust estimation Tyler's scatter estimator majorization-minimization structure constraint estimation theory variance covariance matrix Covariance matrix assessment procedure convex programming matrices

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Optimal Energy Allocation For Delay-Constrained Traffic Over Fading Multiple Access Channels

Optimal Energy Allocation For Delay-Constrained Traffic Over...

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IEEE Global Communications Conference

作者： Antonious M. Girgis Amr El-Keyi Mohammed Nafie Wireless Intell. Networks Center Nile Univ. Cairo Egypt Dept. of Syst. & Comput. Eng. Carleton Univ. Ottawa ON Canada Electron. & Commun. Dept. Cairo Univ. Cairo Egypt

ISBN: (纸本)9781509013296

In this paper, we consider a multiple-access fading channel where N users transmit to a single base station (BS) within a limited number of time slots. We assume that each user has a fixed amount of energy available to be consumed over the transmission window. We derive the optimal energy allocation policy for each user that maximizes the total system throughput under two different assumptions on the channel state information. First, we consider the offline allocation problem where the channel states are known a priori before transmission. We solve a convex optimization problem to maximize the sum-throughput under energy and delay constraints. Next, we consider the online allocation problem, where the channels are causally known to the BS and obtain the optimal energy allocation via dynamic programming when the number of users is small. We also develop a suboptimal resource allocation algorithm whose performance is close to the optimal one. Numerical results are presented showing the superiority of the proposed algorithms over baseline algorithms in various scenarios.

关键词： telecommunication traffic channel allocation convex programming dynamic programming fading channels multi-access systems multiuser channels

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Covariance Control for Discrete-Time Stochastic Linear Systems with Incomplete State Information

Covariance Control for Discrete-Time Stochastic Linear Syste...

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American Control Conference

作者： Efstathios Bakolas Department of Aerospace Engineering and Engineering Mechanics The University of Texas at Austin

ISBN: (纸本)9781509045839

This work deals with a finite-horizon covariance control problem for discrete-time stochastic linear systems with incomplete state information subject to constraints. We show that under the assumption that the class of admissible control policies for this stochastic optimal control problem is comprised of sequences of non-anticipative (causal) control laws that can be expressed as linear combinations of the past and present output measurements of the system, then the covariance control problem can be reduced to a finite-dimensional, deterministic nonlinear program with a convex performance index. In addition, we show that the nonlinear program can be associated with a convex program via a simple relaxation technique that allows us to express the non-convex matrix equality constraint induced by the boundary condition on the terminal state covariance as a positive semi-definite (convex) constraint.

关键词： autocovariance measurement system Nonlinear programming stochastic optimal control convex programming Relaxation Techniques Linear system discrete-time convexity

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COORDINATION BETWEEN TSOs AND DSOs: FLEXIBILITY DOMAIN IDENTIFICATION

COORDINATION BETWEEN TSOs AND DSOs: FLEXIBILITY DOMAIN IDENT...

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The 12th Mediterranean Conference on Power Generation, Transmission, Distribution and Energy Conversion (MEDPOWER 2020)

作者： L. Ageeva M. Majidi D. Pozo Center for Energy Science and Technology Skolkovo Institute of Science and Technology (Skoltech) Moscow Russia Department of Energy Management and Operation of Electrical Networks University of Kassel Kassel Germany

The enormous technological potential accumulated over the past two decades would make possible to change the operating principles of power systems entirely. The consequent technological evolution is not only affecting the structure of the electricity markets, but also the interactions between Transmission System Operators (TSOs) and Distribution System Operators (DSOs). New practical solutions are needed to improve the coordination between the grid operators at the national, TSOs, and local level, DSOs. In this paper, we define the flexibility range of coordination between TSOs and DSOs. By doing so, we propose an algorithm based on epsilon-constrained methods by means of mathematical programming and power systems principles. We evaluate and compare different classical optimal power flow formulations (AC–OPF, DISTFLOW, DISTFLOW–SOCP, and LINDISTFLOW) for building the flexible TSO-DSO flexible domain. The presented approaches in this paper are analyzed in an IEEE 33-bus test radial distribution system. We show that for this particular problem, the DISTFLOW–SOCP has the worst accuracy, despite the popularity among the academic community of convex relaxation approaches.

关键词： load flow power markets mathematical programming convex programming power transmission economics power distribution economics

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Optimization under Uncertainty and Conflict: Algorithms for Heterogenous Quadratic Programs

Optimization under Uncertainty and Conflict: Algorithms for ...

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作者： Wiecek, M. M Clemson Univ SC OFFICE OF NAVAL RESEARCH ARLINGTON VA

Theory and methodology for quadratic programs (QPs) are developed. QPs are formulated with different types of variables, objectives and constraint functions. They have single or multiple objectives modeling conflict, and may carry multiple parameters of two types: one type models unknown or uncertain data while the other is required by the proposed algorithms. The new theory includes derivation of relaxations for nonconvex quadratic functions, bilinear functions, and polynomial functions. The developed algorithms rely on an algorithm for solving the multiparametric linear complementarity problem with sufficient matrices and parameters in general positions, which previously was an unsolved problem.

关键词： Operations research Flow network Integer programming Linear programming Systems engineering Optimization Mathematical programming Evolutionary algorithms Algorithms convex programming Multiobjective optimization Algebraic geometry Complex systems Engineering Mathematics Simplex method Symposia

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Asynchronous Subgradient Methods with Unbounded Delays for Communication Networks

Asynchronous Subgradient Methods with Unbounded Delays for C...

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IEEE Annual Conference on Decision and Control

作者： Nikolaos Gatsis Georgios B. Giannakis Department of Electrical and Computer Engineering University of Minnesota

ISBN: (纸本)9781467320658

Dual decomposition coupled with the subgradient method has found application to optimal resource management in communication networks, as it can lead to distributed and scalable algorithms. Network entities - nodes or functional layers - exchange Lagrange multipliers and primal minimizers of the Lagrangian function towards optimizing a network-wide performance metric. It is of interest to study the performance of the resultant algorithms when such exchanges are delayed or lost. This paper deals with such asynchronous dual subgradient methods in separable convex programming. In this scenario, the subgradient vector is a sum of components, each possibly corresponding to an outdated Lagrange multiplier, and not the current one. A number of network entities is allowed to prematurely stop updating their corresponding variables, thereby effecting infinite delay between the current iterate and the multipliers used for a number of subgradient components. Conditions for convergence of the algorithm are developed. Specific applications include multipath routing in wireline networks and cross-layer optimization in wireless networks. Numerical tests for multipath routing in the Abilene network topology are presented.

关键词： networks(communications) Lagrangian convex programming Telecommunications Gradient Multiplying circuits Lagrange multipliers Asynchronous

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Sparse aperture isar imaging method based on continuous compression sensing

Sparse aperture isar imaging method based on continuous comp...

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IET International Radar Conference (IET IRC 2020)

作者： M. Lv H. Chen X. Zhao L. Zhao P. Xu Radar NCO School of Air Force Early Warning Academy Wuhan People’s Republic of China

In order to solve the problem of scattering point mismatch in high-resolution imaging method based on traditional discrete compression sensing (CS) theory, a sparse aperture ISAR high-resolution imaging method based on continuous compression sensing (CCS) is proposed. Firstly, based on the theory of continuous compressed sensing, the sparse aperture representation model of ISAR imaging is constructed in the continuous atomic domain, and the reconstruction problem of sparse aperture is transformed into solving the atomic norm minimization problem. Then, based on the positive semi-definite property of the atomic norm, the full aperture data recovery is equivalent to the positive semi-definite programming problem, and the improved alternating direction multiplier method is used to solve the sparse optimization problem. Finally, the recovered full aperture data can be recovered, and the IASR imaging result can be achieved via the conventional inverse fast Fourier transform. The sparse reconstruction is implemented directly in the continuous domain, which avoids the degradation of image quality caused by the discretization of the traditional CS method, realizes the high-resolution ISAR imaging under the condition of low measurement, and also has robustness under low SNR. Theoretical analysis and real data experiments verify the effectiveness of the above method.

关键词： synthetic aperture radar radar imaging minimisation compressed sensing image resolution image reconstruction radar resolution fast Fourier transforms image matching image representation mathematical programming convex programming inverse transforms

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convexity and duality in optimization proceedings of the Symposium on convexity and Duality in Optim

Convexity and duality in optimization proceedings of the Sym...

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1985年

作者： Symposium on convexity and Duality in Optimization

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Characterization of banach lattices in terms of quasi-interior points

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International Journal of Mathematics and Mathematical Sciences 2013年第unknown期2013卷 1-11页

作者： Alekhno, Egor A. Faculty of Mechanics and Mathematics Belarusian State University 220030 Minsk Belarus

In terms of quasi-interior points, criteria that a Banach lattice E has order continuous norm or is an AM-space with a unit are given. For example, if E is Dedekind complete and has a weak order unit, then E has order continuous norm if and only if the set of quasi-interior points of E coincides with the set of weak order units of E;a Banach lattice E is an AM-space with a unit x if and only if the set of all quasi-interior points of E coincides with the set {z:x≤z for some >0}. Analogous questions are considered for the case of an ordered Banach space Z with a cone K. Moreover, it is shown that every nonzero point of a cone K≠{0} is quasi-interior if and only if dim Z=1. We also study various -properties of a cone K;in particular, the conditions for which the relation a∧b=0 with a>0 implies that b is not a quasi-interior point are considered. © 2013 Egor A. Alekhno.

关键词： BANACH lattices BANACH algebras LATTICE theory INTERIOR-point methods convex programming MATHEMATICAL optimization

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非正则线性增广拉格朗日乘子法的收敛速率研究（英文）

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高等学校计算数学学报 2022年第1期44卷 36-49页

作者：马峰倪明放火箭军工程大学作战保障学院珠海科技学院

Recently,an indefinite linearized augmented Lagrangian method(ILALM) was proposed for the convex programming problems with linear *** IL-ALM differs from the linearized augmented Lagrangian method in that the augmented Lagrangian is linearized by adding an indefinite quadratic proximal ***,it preserves the algorithmic feature of the linearized ALM and usually has the advantage to improve the *** IL-ALM is proved to be convergent from contraction perspective,but its convergence rate is still *** is mainly because that the indefinite setting destroys the structures when we directly employ the contraction *** this paper,we derive the convergence rate for this algorithm by using a different *** prove that a worst-case O(1/t)convergence rate is still hold for this algorithm,where t is the number of *** we show that the customized proximal point algorithm can employ larger step sizes by proving its equivalence to the linearized ALM.

关键词： convex programming augmented Lagrangian method proximal point algorithm convergence analysis indefinite regularization

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