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In this paper, low-complexity joint power assignment algorithms are developed for multi-source multi-destination relay networks where multiple sources share a common relay that forwards all received signals simultaneously to destinations. In particular, we consider the following power optimization strategies: (i) Minimization of the total transmission power of the sources and the relay under the constraint that the signal-to-interference-plus-noise ratio (SINR) requirement of each source-destination pair is satisfied, and (ii) Maximization of the minimum SINR among all source-destination pairs subject to any given total power budget. Both optimization problems involve K power variables, where K is the number of source-destination pairs in the network, and an exhaustive search is prohibitive for large K. In this work, we develop a methodology that allows us to obtain an asymptotically tight approximation of the SINR and reformulate the original optimization problems to single-variable optimization problems, which can be easily solved by numerical search of the single variable. Then, the corresponding optimal transmission power at each source and relay can be calculated directly. The proposed optimization schemes are scalable and lead to power assignment algorithms that exhibit the same optimization complexity for any number (K) of source-destination pairs in the network. Moreover, we apply the methodology that we developed to solve a related max-min SINR based optimization problem in which we determine power assignment for the sources and the relay to maximize the minimum SINR among all source-destination pairs subject to any given total power budget. Extensive numerical studies illustrate and validate our theoretical developments. [ABSTRACT FROM AUTHOR]

Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop an algorithm for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes. [ABSTRACT FROM AUTHOR]

Abstract: This article considers recovery of signals that are sparse or approximately sparse in terms of a (possibly) highly overcomplete and coherent tight frame from undersampled data corrupted with additive noise. We show that the properly constrained -analysis optimization problem, called analysis Dantzig selector, stably recovers a signal which is nearly sparse in terms of a tight frame provided that the measurement matrix satisfies a restricted isometry property adapted to the tight frame. As a special case, we consider the Gaussian noise. Further, under a sparsity scenario, with high probability, the recovery error from noisy data is within a log-like factor of the minimax risk over the class of vectors which are at most s sparse in terms of the tight frame. Similar results for the analysis LASSO are shown. The above two algorithms provide guarantees only for noise that is bounded or bounded with high probability (for example, Gaussian noise). However, when the underlying measurements are corrupted by sparse noise, these algorithms perform suboptimally. We propose new algorithms for reconstructing signals that are nearly sparse in terms of a tight frame in the presence of bounded noise combined with sparse noise, and present corresponding recovery guarantees. The analysis in this paper is based on the restricted isometry property adapted to a tight frame, which is a natural extension to the standard restricted isometry property. [Copyright &y& Elsevier]

This paper proposes a new approximation scheme which is an extension to the well-established Charef s approximation method for fractional order systems. The method relaxes the constraints on the locations of the pole-zero pairs of the approximate system, which provides more flexibility and space for approximate system to approach the original system as close as possible. The approxi-mate system based on an optimization process performs not only a good magnitude fitting but also a good phase fitting. The benefits from using the proposed scheme are illustrated by numerical examples in frequency domains. [ABSTRACT FROM AUTHOR]

Extensible processors are increasingly becoming popular as they allow for incorporating custom instructions to meet design constraints. Identifying custom instructions is a time-consuming process particularly when large applications are considered. In this study, efficient techniques for identifying custom instruction candidates are proposed. New pruning criteria are introduced and combined with the latest work cited in the literature to accelerate the identification process. The proposed techniques have been shown to be capable of enumerating all valid patterns corresponding to given micro-architectural constraints with reduced search space. Experimental results show that, the proposed algorithm is capable of reducing the runtime by up to 50% for the case of single-output constraint, and by up to 44% for the case of multiple-output constraint. In addition, an approximation algorithm is also proposed to select the valid pattern that provides for maximum gain in execution of applications. In particular, the proposed algorithm focuses on the promising candidates, instead of enumerating all valid patterns as was the case in previous algorithms. It has been shown to be capable of obtaining the optimal valid pattern for most cases of I/O constraints and the runtime has been reduced by up to 90% for some I/O constraints. [ABSTRACT FROM AUTHOR]