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The fundamental theorem of linear programming: extensions and applications

OPTIMIZATION 2011年第1-2期60卷 283-301页

作者： Tardella, F. Fac Econ I-00161 Rome Italy

The fundamental theorem of linear programming (LP) states that every feasible linear program that is bounded below has an optimal solution in a zero-dimensional face (a vertex) of the feasible polyhedron. We extend this result in two directions. We find a larger class of objective functions for which vertex optimality holds, and we give conditions guaranteeing the existence of an optimal solution in a larger family of faces of the feasible polyhedron. Our results also extend, with a very simple proof, the Frank-Wolfe theorem on the existence of an optimal solution to a Quadratic Program that is bounded below. We then apply our results to build up a general framework for obtaining upper and lower bounds and constant factor approximation algorithms for optimization problems. Furthermore, we show that several known results providing continuous formulations for discrete optimization problems can be easily derived and generalized with our extension of the fundamental theorem of Linear programming. Finally, by exploiting the equivalence between continuous and discrete formulations of the problem of minimizing a function on a polyhedron, we prove polynomial-time solvability and present efficient algorithms for several new classes of continuous optimization problems.

关键词： fundamental theorem of linear programming concave programming quadratic programming approximation algorithms maximum clique pseudo-Boolean optimization

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Large-scale multi-zone optimal power dispatch using hybrid hierarchical evolution technique

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JOURNAL OF ENGINEERING-JOE 2014年第3期2014卷 71-80页

作者： Pandit, Manjaree Srivastava, Laxmi Sharma, Manisha Dubey, Hari Mohan Panigrahi, Bijaya Ketan MITS Dept Elect Engn Gwalior India IIT Dept Elect Engn Delhi India

A new hybrid technique based on hierarchical evolution is proposed for large, non-convex, multi-zone economic dispatch (MZED) problems considering all practical constraints. Evolutionary/swarm intelligence-based optimisation techniques are reported to be effective only for small/medium-sized power systems. The proposed hybrid hierarchical evolution (HHE) algorithm is specifically developed for solving large systems. The HHE integrates the exploration and exploitation capabilities of particle swarm optimisation and differential evolution in a novel manner such that the search efficiency is improved substantially. Most hybrid techniques export or exchange features or operations from one algorithm to the other, but in HHE their entire individual features are retained. The effectiveness of the proposed algorithm has been verified on six-test systems having different sizes and complexity levels. Non-convex MZED solution for such large and complex systems has not yet been reported.

关键词： load dispatching concave programming evolutionary computation particle swarm optimisation large-scale multizone optimal power dispatch non-convex MZED problems hybrid hierarchical evolution technique HHE evolutionary optimisation swarm intelligence-based optimisation particle swarm optimisation differential evolution six-test systems

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Semistability-Based Robust and Optimal Control Design for Network Systems

Semistability-Based Robust and Optimal Control Design for Ne...

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51st IEEE Annual Conference on Decision and Control (CDC)

作者： Hui, Qing Liu, Zhenyi Texas Tech Univ Dept Mech Engn Lubbock TX 79409 USA

ISBN: (纸本)9781467320665

In this paper, we present a new Linear-Quadratic Semistabilizers (LQS) theory for linear network systems. This new semistable H-2 control framework is developed to address the robust and optimal semistable control issues of network systems while preserving network topology subject to white noise. Two new notions of semistabilizability and semicontrollability are introduced as a means to connecting semistability with the Lyapunov equation based technique. With these new notions, we first develop a semistable H-2 control theory for network systems by exploiting the properties of semistability. A new series of necessary and sufficient conditions for semistability of the closed-loop system have been derived in terms of the Lyapunov equation. Based on these results, we propose a constrained optimization technique to solve the semistable H-2 networktopology- preserving control design for network systems. Then optimization analysis and the development of numerical algorithms for the obtained constrained optimization problem are conducted. We establish the existence of optimal solutions for the obtained nonconvex optimization problem. Next, we propose a swarm optimization based numerical algorithm towards efficiently solving this nonconvex, nonlinear optimization problem due to the strong resemblance between swarm behaviors in nature and the notion of semistability. Finally, several numerical examples will be provided to illustrate the effectiveness of the proposed method.

关键词： H2 control Lyapunov methods closed loop systems concave programming control system synthesis controllability linear quadratic control network topology networked control systems robust control

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On Ergodic Secrecy Capacity of Fast Fading MIMOME Wiretap Channel With Statistical CSIT

On Ergodic Secrecy Capacity of Fast Fading MIMOME Wiretap Ch...

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Annual Summit and Conference of the Asia-Pacific-Signal-and-Information-Processing-Association (APSIPA)

作者： Lin, Shih-Chun Natl Taiwan Univ Sci & Technol Dept Elect & Comp Engn Taipei 10607 Taiwan

ISBN: (纸本)9789869000604

In this paper, we consider the secure transmission in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity result with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is forming an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of which the same as the eavesdropper's channel matrix. Next, subject to the total power constraint overall transmit antennas, we solve the channel-input covariance matrix optimization problem to fully characterize the MIMOME secrecy capacity. Typically, the MIMOME optimization problems are non-concave. However, with aids of the proposed degraded channel, we show that the stochastic MIMOME optimization problem can be transformed to be a Schur-concave problem to find its optimal solution. Finally, we find that the MIMOME secrecy capacities scale with the signal-to-noise ratios with large enough numbers of antennas at legitimate receiver. However, as shown in previous works, such a scaling does not exist for wiretap channels with single antenna at legitimate receiver and eavesdropper each.

关键词： MIMO communication Rayleigh channels channel capacity concave programming covariance matrices cryptography radio receivers radio transmitters statistical analysis stochastic processes telecommunication security

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Distributed Solution for a Maximum Variance Unfolding Problem with Sensor and Robotic Network Applications

Distributed Solution for a Maximum Variance Unfolding Proble...

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50th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

作者： Simonetto, Andrea Keviczky, Tamas Dimarogonas, Dimos V. Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands

ISBN: (纸本)9781467345392;9781467345378

We focus on a particular non-convex networked optimization problem, known as the Maximum Variance Unfolding problem and its dual, the Fastest Mixing Markov Process problem. These problems are of relevance for sensor networks and robotic applications. We propose to solve both these problems with the same distributed primal-dual subgradient iterations whose convergence is proven even in the case of approximation errors in the calculation of the subgradients. Furthermore, we illustrate the use of the algorithm for sensor network applications, such as localization problems, and for mobile robotic networks applications, such as dispersion problems.

关键词： Markov processes approximation theory concave programming convergence distributed sensors iterative methods mobile robots sensors

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An optimization-based demand response in radial distribution networks

An optimization-based demand response in radial distribution...

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IEEE Globecom Workshops (GC Wkshps)

作者： Li, Na Gan, Lingwen Chen, Lijun Low, Steven H. CALTECH Div Engn & Appl Sci Pasadena CA 91125 USA Univ Colorado Coll Engn & Appl Sci Boulder CO 80309 USA

ISBN: (纸本)9781467349413;9781467349420

Demand response has recently become a topic of active research. Most of work however considers only the balance between aggregate load and supply, and abstracts away the underlying power network and the associated power flow constraints and operating constraints. In this paper, we study demand response in a radial distribution network, by formulating it as an optimal power flow problem that maximizes the aggregate user utilities and minimizes the power line losses, subject to the power flow constraints and operating constraints. As the resulting problem is non-convex and difficult to solve, we propose a convex relaxation that is usually exact for the real-world distribution circuits. We then propose a distributed algorithm for the load-serving entity to set the price signal to coordinate the users' demand response so as to achieve the optimum. Numerical examples show that the proposed algorithm converges fast for real-world distribution systems.

关键词： concave programming convex programming demand side management distributed algorithms distribution networks load flow minimisation power cables

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Joint Transmit Beamforming and Antenna Selection for Energy Efficiency Maximization in MISO Downlink

Joint Transmit Beamforming and Antenna Selection for Energy ...

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IEEE Global Conference on Signal and Information Processing (GlobalSIP)

作者： Tervo, Oskari Tran, Le-Nam Juntti, Markku Univ Oulu Ctr Wireless Commun POB 4500 FI-90014 Oulu Finland Natl Univ Ireland Maynooth Dept Elect Engn Maynooth Kildare Ireland

ISBN: (纸本)9781479970889

We study the joint beamforming and antenna selection problem for energy efficiency maximization in multi-user multiple-input single-output (MISO) downlink channel. By viewing antenna selection as finding a sparse solution, we first introduce a sparsity-inducing regularization term to the design problem. Since the resulting problem is nonconvex, it is difficult to find an optimal solution, and we apply a local optimization method based on the concept of sequential convex approximation (SCA) to solve this problem. By proper reformulations we arrive at a fast converging iterative algorithm, where a convex program is solved at each iteration. In the first design, we simply ignore antennas of which the associated beamformers are nearly zero and select the remaining ones. In the second design, we further perform the search over the selected antennas of the first design to improve the energy efficiency. Numerical results demonstrate remarkable performance gains of the proposed approaches in terms of energy efficiency over the solution without antenna selection.

关键词： antennas approximation theory array signal processing concave programming convergence of numerical methods convex programming iterative methods wireless channels MISO downlink channel antenna selection problem convex program design problem energy efficiency improvement energy efficiency maximization fast converging iterative algorithm joint transmit beamforming local optimization method multiuser multiple-input single-output downlink channel nonconvex problem performance gains sequential convex approximation concept sparsity-inducing regularization term Algorithm design and analysis Approximation methods Convergence Power demand Signal processing algorithms Transmitting antennas Energy efficiency ANTENNA convex programming convergence of numerical methods Algorithm design and analysis design problems transmitting antennas Signal processing algorithms iterative methods Power demand wireless channels Approximation method array signal processing Approximation Theory multiple-input single-output

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Convex Relaxation and Decomposition in Large Resistive Power Networks with Energy Storage

Convex Relaxation and Decomposition in Large Resistive Power...

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IEEE International Conference on Smart Grid Communications (SmartGridComm)

作者： Lou, Xin Tan, Chee Wei City Univ Hong Kong Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9781479915262

A fundamental challenge of a smart grid is: to what extent can moving energy through space and time be optimized to benefit the power network with large-scale storage integration? In this paper, we study a dynamic optimal power flow problem with energy storage dynamics in resistive power networks. We first propose a second order cone programming convex relaxation to solve this nonconvex problem optimally. Then, we apply optimization decomposition techniques to decompose and decouple the problem and obtain the global optimal solution in a distributed manner. The optimization decomposition offers new interesting insight over space and time between the dual solution and energy storage dynamics. We investigate the efficiency of the SOCP relaxation in several IEEE benchmark systems and verify that the distributed algorithms can converge fast to the global optimal solution by numerical simulations.

关键词： IEEE standards concave programming convex programming decomposition distributed algorithms distribution networks energy storage load flow relaxation theory smart power grids transmission networks

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Power Efficient MISO Beamforming for Secure Layered Transmission

Power Efficient MISO Beamforming for Secure Layered Transmis...

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IEEE Wireless Communications and Networking Conference (WCNC)

作者： Ng, Derrick Wing Kwan Schober, Robert Alnuweiri, Hussein FAU Inst Digital Commun Erlangen Germany Texas A&M Univ Qatar Doha Qatar Univ British Columbia Vancouver BC Canada

ISBN: (纸本)9781479930838

This paper studies secure layered video transmission in a multiuser multiple-input single-output (MISO) beamforming downlink conununication system. The power allocation algorithm design is formulated as a non-convex optimization problem for minimizing the total transmit power while guaranteeing a minimum received signal-to-interference-plus-noise ratio (SINR) at the desired receiver. In particular, the proposed problem formulation takes into account the self-protecting architecture of layered transmission and artificial noise generation to prevent potential information eavesdropping. A semi-definite programming (SDP) relaxation based power allocation algorithm is proposed to obtain an upper bound solution. A sufficient condition for the global optimal solution is examined to reveal the tightness of the upper bound solution. Subsequently, two subopthnal power allocation schemes with low computational complexity are proposed for enabling secure layered video transmission. Simulation results demonstrate significant transmit power savings achieved by the proposed algorithms and layered transmission compared to the baseline schemes.

关键词： array signal processing communication complexity concave programming multi-access systems resource allocation telecommunication power management telecommunication security SDP SINR artificial noise generation computational complexity multiuser multiple-input single-output beamforming nonconvex optimization power allocation algorithm power efficient MISO beamforming secure layered transmission secure layered video transmission semidefinite programming signal-to-interference-plus-noise ratio Noise Optimization Receivers Resource management Streaming media Transmitters Vectors SINR Multi access systems management of resources Streaming Video telecommunication security layered transmission Service Discovery Protocol communication complexity array signal processing complexity classes Receivers Transmitters Resource utilization multiple-input single-output Noise

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Joint Optimization of Detection and Power Allocation for OFDM-based Cognitive Radios

Joint Optimization of Detection and Power Allocation for OFD...

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IEEE Global Telecommunications Conference (GLOBECOM 2010)

作者： Huang, Xiaoge Beferull-Lozano, Baltasar Univ Valencia IRTIC Grp Informat & Commun Syst GSIC Paterna 46980 Valencia Spain

ISBN: (纸本)9781424456383

Efficient spectrum sensing ensures cognitive radio (CR) users opportunistically use the under-utilized frequency band without causing harmful interference to primary users (PUs). However, in practice, owing to the non-zero probability of the missed detection and false alarm of active primary transmission, a certain degree of performance degradation of the PU is unavoidable. In this paper, we consider OFDM-based communication systems and present efficient algorithms to maximize the total throughput of the CR by optimizing jointly both the detection operation and the power allocation, taking into account the influence of the probabilities of missed detection and false alarm. The optimization problem can be formulated as a two-variable non-convex problem, which can be solved approximately by using an alternating direction optimization (ADO) method. A novel criterion is introduced to ensure that the performance degradation of the PU is bounded properly. First, we analyze the case of only one CR and then we generalize to the case of a two CR non-cooperative power allocation game, showing that a Nash equilibrium (NE) can be achieved in few iterations by using an iterative ADO method. Simulation results demonstrate that the proposed solution can considerably improve system performance.

关键词： CR user Nash equilibrium OFDM modulation OFDM-based cognitive radio alternating direction optimization method cognitive radio concave programming false alarm probability frequency allocation game theory iterative ADO method iterative methods missed detect

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