The aim of this paper is to present a proposal for convex optimization, based on linear programming, for blind equalizers applied to digital communication systems. Different to solutions that have been presented in th...
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The aim of this paper is to present a proposal for convex optimization, based on linear programming, for blind equalizers applied to digital communication systems. Different to solutions that have been presented in the literature using linear programming, the proposed model takes into consideration channels with intersymbol interference and Gaussian additive noise. The work also provides a comparative evaluation of the performance of interior-point, active-set, and simplex methods applied to the optimization process involving the blind equalizer. The results of simulations for different digital communication systems are presented using bit error rate performance curves. (C) 2014 Elsevier GmbH. All rights reserved.
In designing discrete-time filters, the length of the impulse response is often used as an indication of computational cost. In systems where the complexity is dominated by arithmetic operations, the number of nonzero...
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In designing discrete-time filters, the length of the impulse response is often used as an indication of computational cost. In systems where the complexity is dominated by arithmetic operations, the number of nonzero coefficients in the impulse response may be a more appropriate metric to consider instead, and computational savings are realized by omitting arithmetic operations associated with zero-valued coefficients. This metric is particularly relevant to the design of sensor arrays, where a set of array weights with many zero-valued entries allows for the elimination of physical array elements, resulting in a reduction of data acquisition and communication costs. However, designing a filter with the fewest number of nonzero coefficients subject to a set of frequency-domain constraints is a computationally difficult optimization problem. This paper describes several approximate polynomial-time algorithms that use linear programming to design filters having a small number of nonzero coefficients, i.e., filters that are sparse. Specifically, we present two approaches that have different computational complexities in terms of the number of required linear programs. The first technique iteratively thins the impulse response of a non-sparse filter until frequency-domain constraints are violated. The second minimizes the 1-norm of the impulse response of the filter, using the resulting design to determine the coefficients that are constrained to zero in a subsequent re-optimization stage. The algorithms are evaluated within the contexts of array design and acoustic equalization.
By linear programming system identification, we mean the problem of estimating the objective function coefficient vector pi and the technological coefficient matrix A for a linear programming system that best explains...
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By linear programming system identification, we mean the problem of estimating the objective function coefficient vector pi and the technological coefficient matrix A for a linear programming system that best explains a set of input-output vectors. Input vectors are regarded as available resources. Output vectors are compared to imputed optimal ones by a decisional efficiency measure and a likelihood function is constructed. In an earlier paper, we obtained results for a simplified version of the problem. In this paper, we propose a genetic algorithm approach for the general case in which pi and A are of arbitrary finite dimensions and have nonnegative components. A method based on Householder transformations and Monte Carlo integration is used as an alternative to combinatorial algorithms for the extreme points and volumes of certain required convex polyhedral sets. The method exhibits excellent face validity for a published test data set in data envelopment analysis. (c) 2007 Elsevier B.V. All rights reserved.
Several logics for reasoning under uncertainty distribute ''probability mass'' over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions...
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Several logics for reasoning under uncertainty distribute ''probability mass'' over sets in some sense. These include probabilistic logic, Dempster-Shafer theory, other logics based on belief functions, and second-order probabilistic logic. We show that these logics are instances of a certain type of linear programming model, typically with exponentially many variables. We also show how a single linear programming package can implement these logics computationally if one ''plugs in'' a different column generation subroutine for each logic, although the practicality of this approach has been demonstrated so far only for probabilistic logic.
At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of...
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At the beginning of the 13th century Fibonacci described the rules for making mixtures of all kinds, using the Hindu-Arabic system of arithmetic. His work was repeated in the early printed books of arithmetic, many of which contained chapters on 'alligation', as the subject became known. But the rules were expressed in words, so the subject often appeared difficult, and occasionally mysterious. Some clarity began to appear when Thomas Harriot introduced a modern form of algebraic notation around 1600, and he was almost certainly the first to express the basic rule of alligation in algebraic terms. Thus a link was forged with the work on Diophantine problems that occupied mathematicians like John Pell and John Kersey in the 17th century. Joseph Fourier's work on mechanics led him to suggest a procedure for handling linear inequalities based on a combination of logic and algebra;he also introduced the idea of describing the set of feasible solutions geometrically. In 1898, inspired by Fourier's work, Gyula Farkas proved a fundamental theorem about systems of linear inequalities. This topic eventually found many applications, and it became known as linear programming. The theorem of Farkas also plays a significant role in Game Theory.
Recently there has been great interest in establishing the color gamut of solid colors or the optimum colors. The optimum colors are widely used for quantifying the quality of light sources and evaluating reproduction...
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Recently there has been great interest in establishing the color gamut of solid colors or the optimum colors. The optimum colors are widely used for quantifying the quality of light sources and evaluating reproduction devices. An enumeration method was developed by Martinez-Verdu et al. [J. Opt. Soc. Am. A 24, 1501 (2007)] for finding optimum colors. However, it was found that the method is too time-costly. In this paper, a linear programming approach is proposed. The proposed method is simple and faster and has the advantage of keeping the characteristics of the true boundary. Comparison of the present method with the method of Martinez-Verdu et al. is also given. (C) 2010 Optical Society of America
Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few app...
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Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for obtaining high-quality solutions. In this study, grid-based approximations are used in combination with linear programming (LP) models to generate approximate policies for CPOMDPs. A detailed numerical study is conducted with six CPOMDP problem instances considering both their finite and infinite horizon formulations. The quality of approximation algorithms for solving unconstrained POMDP problems is established through a comparative analysis with exact solution methods. Then, the performance of the LP-based CPOMDP solution approaches for varying budget levels is evaluated. Finally, the flexibility of LP-based approaches is demonstrated by applying deterministic policy constraints, and a detailed investigation into their impact on rewards and CPU run time is provided. For most of the finite horizon problems, deterministic policy constraints are found to have little impact on expected reward, but they introduce a significant increase to CPU run time. For infinite horizon problems, the reverse is observed: deterministic policies tend to yield lower expected total rewards than their stochastic counterparts, but the impact of deterministic constraints on CPU run time is negligible in this case. Overall, these results demonstrate that LP models can effectively generate approximate policies for both finite and infinite horizon problems while providing the flexibility to incorporate various additional constraints into the underlying model.
A pattern synthesis technique for arbitrary planar arrays which are characterised in terms of a generalised scattering matrix and whose radiated field is expressed as a spherical mode expansion is introduced. The proc...
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A pattern synthesis technique for arbitrary planar arrays which are characterised in terms of a generalised scattering matrix and whose radiated field is expressed as a spherical mode expansion is introduced. The procedure yields the complex-valued excitations to achieve a minimum-maximum sidelobe level given a specified pointing direction and mainlobe width, as well as prescribed field nulls. All inter-element coupling effects coming from complex radiating structures used as array elements are inherently taken into account. Numerical results are presented for arrays of dielectric resonator antennas.
A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L1 norm and then transforming the resulting quadratic o...
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A linear programming (LP) approach is proposed for the weighted graph matching problem. A linear program is obtained by formulating the graph matching problem in L1 norm and then transforming the resulting quadratic optimization problem to a linear one. The linear program is solved using a Simplex-based algorithm. Then, approximate 0-1 integer solutions are obtained by applying the Hungarian method on the real solutions of the linear program. The complexity of the proposed algorithm is polynomial time, and it is O(n6 L) for matching graphs of size n. The developed algorithm is compared to two other algorithms. One is based on an eigendecomposition approach and the other on a symmetric polynomial transform. Experimental results showed that the LP approach is superior in matching graphs than both other methods.
We give a new derivation of the linear program corresponding to a Markov Decision Process (MDP) in steady state, which seeks to minimize discounted total expected cost. We use this derivation to show, very directly, t...
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We give a new derivation of the linear program corresponding to a Markov Decision Process (MDP) in steady state, which seeks to minimize discounted total expected cost. We use this derivation to show, very directly, the known relationship between this linear program and the one corresponding to an MDP which seeks to minimize average expected cost. The usefulness of this approach in a practical setting is briefly discussed.
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