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This paper presents a family of robust set-membership normalized subband adaptive filtering (RSM-NSAF) algorithms for acoustic echo cancellation (AEC). By using a new robust set-membership error bound, the RSM-NSAF algorithm obtains improved robustness against impulsive noises and decreased steady-state misalignment relative to the conventional set-membership NSAF (SM-NSAF) algorithm. To exploit the sparsity of the impulse response, the L0 norm constraint robust set-membership NSAF ( L0 -RSM-NSAF), robust set-membership improved proportionate NSAF (RSM-IPNSAF), and L0 norm constraint robust set-membership improved proportionate NSAF ( L0 -RSM-IPNSAF) algorithms are derived by minimizing a differentiable cost function that utilizes the Riemannian distance between the updated and previous weight vectors as well as the L0 norm of the weighted updated weight vector. Simulations in AEC application confirm the improvements of the proposed algorithms in performance. [ABSTRACT FROM PUBLISHER]

Many problems of interest for cyber-physical network systems can be formulated as mixed-integer linear programs in which the constraints are distributed among the agents. In this paper, we propose a distributed algorithmic framework to solve this class of optimization problems in a peer-to-peer network with no coordinator and with limited computation and communication capabilities. At each communication round, agents locally solve a small linear program, generate suitable cutting planes, and communicate a fixed number of active constraints. Within the distributed framework, we first propose an algorithm that, under the assumption of integer-valued optimal cost, guarantees finite-time convergence to an optimal solution. Second, we propose an algorithm for general problems that provides a suboptimal solution up to a given tolerance in a finite number of communication rounds. Both algorithms work under asynchronous, directed, unreliable networks. Finally, through numerical computations, we analyze the algorithm scalability in terms of the network size. Moreover, for a multi-agent multi-task assignment problem, we show, consistently with the theory, its robustness to packet loss. [ABSTRACT FROM AUTHOR]

This paper considers an unconstrained collaborative optimization of a sum of convex functions, where agents make decisions using local information in the presence of random interconnection topologies. We recast the problem as minimization of the sum of convex functions over a constraint set defined as the set of fixed-value points of a random operator derived from weighted matrices of random graphs. We show that the derived random operator has nonexpansivity property; therefore, this formulation does not need the distribution of random communication topologies. Hence, it includes random networks with/without asynchronous protocols. As an extension of the problem, we define a novel optimization problem, namely minimization of a convex function over the fixed-value point set of a nonexpansive random operator. We propose a discrete-time algorithm using diminishing step size for converging almost surely and in mean square to the global solution of the optimization problem under suitable assumptions. Consequently, as a special case, it reduces to a totally asynchronous algorithm for the distributed optimization problem. We show that fixed-value point is a bridge from deterministic analysis to random analysis of the algorithm. Finally, a numerical example illustrates the convergence of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of achieving average consensus over a random time-varying sequence of directed graphs by extending the class of so-called push-sum algorithms to such random scenarios. Provided that an ergodicity notion, which we term the directed infinite flow property, holds and the auxiliary states of agents are uniformly bounded away from zero infinitely often, we prove the almost sure convergence of the evolutions of this class of algorithms to the average of initial states. Moreover, for a random sequence of graphs generated using a so-called time-varying $B$ -irreducible probability matrix, we establish convergence rates for the proposed push-sum algorithm. [ABSTRACT FROM AUTHOR]

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a solution can be based on prior functions. We show that the problem is well-posed when formulated in a parametric fashion, and that the solution parameter depends continuously on the prior function. In this way, we are able to obtain a smooth parametrization of admissible spectral densities. Based on this result, the problem is reparametrized via a bijective change of variables out of a numerical consideration, and then a continuation method is used to compute the unique solution parameter. Numerical aspects, such as convergence of the proposed algorithm and certain computational procedures are addressed. A simple example is provided to show the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

The limited memory version of the Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm is the most popular quasi-Newton algorithm in machine learning and optimization. Recently, it was shown that the stochastic L-BFGS (sL-BFGS) algorithm with the variance-reduced stochastic gradient converges linearly. In this paper, we propose a new sL-BFGS algorithm by importing a proper momentum. We prove an accelerated linear convergence rate under mild conditions. The experimental results on different data sets also verify this acceleration advantage. [ABSTRACT FROM AUTHOR]

In this paper, we propose a distributed Newton method for decenteralized optimization of large sums of convex functions. Our proposed method is based on creating a set of separable finite sum minimization problems by utilizing a decomposition technique known as Global Consensus that distributes the computation across nodes of a graph and enforces a consensus constraint among the separated variables. The key idea is to exploit the sparsity of the dual Hessian and recast the computation of the Newton step as one of the efficiently solving symmetric diagonally dominant linear equations. We show that our method outperforms the state-of-the-art algorithms, including ADMM. We validate our algorithm both theoretically and empirically. On the theory side, we demonstrate that our algorithm exhibits superlinear convergence within a neighborhood of optimality. Empirically, we show the superiority of this new method on a variety of large-scale optimization problems. The proposed approach is scalable to large problems and has a low communication overhead. [ABSTRACT FROM AUTHOR]

This article proposes a robust method for the synthesis and design of optimal linear group delay filters with prescribed bandwidth and dispersion properties. The proposed filters are based on a cascade of second-order all-pass filter cells, for which all the parameters are optimized in order to reach the desired wideband linear group delay characteristic with positive slope. Compared to the previously published synthesis method, the proposed approach offers appropriate initialization enabling convergence and aiming for the optimal solution. The method’s convergence and robustness are proved through a 21-cells synthesis, which is the highest number of cascaded cells reported to date, due to the usual convergence problem. Then the electronic feasibility is illustrated through the measurement results of a lumped-elements linear group-delay filter prototype dimensioned with this method. The measured group delay presents a positive slope of 8 ns GHz−1 in the frequency range [100–725] MHz. It is, to the best of our knowledge, the highest positive slope reported to date with an electronic implementation (i.e except SAW and waveguide devices). [ABSTRACT FROM AUTHOR]

Conjugate gradient (CG) methods are a class of important methods for solving linear equations and nonlinear optimization problems. In this paper, we propose a new stochastic CG algorithm with variance reduction and we prove its linear convergence with the Fletcher and Reeves method for strongly convex and smooth functions. We experimentally demonstrate that the CG with variance reduction algorithm converges faster than its counterparts for four learning models, which may be convex, nonconvex or nonsmooth. In addition, its area under the curve performance on six large-scale data sets is comparable to that of the LIBLINEAR solver for the $L2$ -regularized $L2$ -loss but with a significant improvement in computational efficiency. 1 CGVR algorithm is available on github: https://github.com/xbjin/cgvr [ABSTRACT FROM AUTHOR]

This paper considers the problem of a leader that seeks to optimally influence the opinions of agents in a directed network through connecting with a limited number of the agents (“direct followers”), possibly in the presence of a fixed competing leader. The settings involving a single leader and two competing leaders are unified into a general combinatoric optimization problem, for which two heuristic approaches are developed. The first approach is based on a convex relaxation scheme, possibly in combination with the $\ell _1$ -norm regularization technique, and the second is based on a greedy selection strategy. The main technical novelties of this work are in the establishment of supermodularity of the objective function and convexity of its continuous relaxation. The greedy approach is guaranteed to have a lower bound on the approximation ratio sharper than $(1-1/e)$ , while the convex approach can benefit from efficient (customized) numerical solvers to have practically comparable solutions possibly with faster computation times. The two approaches can be combined to provide improved results. In numerical examples, the approximation ratio can be made to reach ${\text{90}\%}$ or higher depending on the number of direct followers. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed model predictive control (MPC) approach for a family of discrete-time linear systems with local (uncoupled) and global (coupled) constraints. The proposed approach is based on the dual problem of an overall MPC optimization problem involving all systems, which is then solved distributively using a modified distributed Nesterov-accelerated-gradient algorithm. To further reduce the computational requirement, this approach allows for early termination of the distributed gradient algorithm. This is made possible via a consensus algorithm that determines the satisfaction of the termination condition and by appropriate tightening of the coupled constraints. Under reasonable assumptions, the approach is able to produce a suboptimal solution as long as the network of the systems is connected while ensuring recursive feasibility and exponential stability of the closed-loop system. The performance of the proposed approach is demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

Consider a connected network of agents endowed with local cost functions representing private objectives. Agents seek to find an agreement on some minimizer of the aggregate cost, by means of repeated communications between neighbors. Consensus on the average over the network, usually addressed by gossip algorithms, is a special instance of this problem, corresponding to quadratic private objectives. Consensus on the median, or more generally, consensus on a given quantile, is also a special instance of this problem. In this paper we show that optimizing the aggregate cost function regularized by a total variation (TV) term has appealing properties. First, it can be done very naturally in a distributed way, yielding algorithms that are efficient on numerical simulations. Secondly, the optimum for the regularized cost is shown to be also the optimum for the initial aggregate cost function under assumptions that are simple to state. Finally, these algorithms are robust to unreliable agents that keep injecting some false value in the network. This is remarkable enough, and is not the case, for instance, of gossip algorithms that are entirely ruled by unreliable agents as detailed in the paper. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the learning problem of multilayer perceptrons (MLPs) formulated as the problem of minimizing a smooth error function. As well known, the learning problem of MLPs can be a difficult nonlinear nonconvex optimization problem. Typical difficulties can be the presence of extensive flat regions and steep sided valleys in the error surface, and the possible large number of training data and of free network parameters. We define a wide class of batch learning algorithms for MLP, based on the use of block decomposition techniques in the minimization of the error function. The learning problem is decomposed into a sequence of smaller and structured minimization problems in order to advantageously exploit the structure of the objective function. Theoretical convergence results are established, and a specific algorithm is constructed and evaluated through an extensive numerical experimentation. The comparisons with the state-of-the-art learning algorithms show the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

In many real-world applications, data are represented by matrices or high-order tensors. Despite the promising performance, the existing 2-D discriminant analysis algorithms employ a single projection model to exploit the discriminant information for projection, making the model less flexible. In this paper, we propose a novel compound rank- $k$ projection (CRP) algorithm for bilinear analysis. The CRP deals with matrices directly without transforming them into vectors, and it, therefore, preserves the correlations within the matrix and decreases the computation complexity. Different from the existing 2-D discriminant analysis algorithms, objective function values of CRP increase monotonically. In addition, the CRP utilizes multiple rank- $k$ projection models to enable a larger search space in which the optimal solution can be found. In this way, the discriminant ability is enhanced. We have tested our approach on five data sets, including UUIm, CVL, Pointing’04, USPS, and Coil20. Experimental results show that the performance of our proposed CRP performs better than other algorithms in terms of classification accuracy. [ABSTRACT FROM PUBLISHER]

Nonnegative matrix factorization (NMF) has recently become a very popular unsupervised learning method because of its representational properties of factors and simple multiplicative update algorithms for solving the NMF. However, for the common NMF approach of minimizing the Euclidean distance between approximate and true values, the convergence of multiplicative update algorithms has not been well resolved. This paper first discusses the convergence of existing multiplicative update algorithms. We then propose a new multiplicative update algorithm for minimizing the Euclidean distance between approximate and true values. Based on the optimization principle and the auxiliary function method, we prove that our new algorithm not only converges to a stationary point, but also does faster than existing ones. To verify our theoretical results, the experiments on three data sets have been conducted by comparing our proposed algorithm with other existing methods. [ABSTRACT FROM AUTHOR]