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Dual Coordinate Descent (DCD) is one of the most popular optimization methods. The parallelization of DCD is difficult, as DCD is sequential in nature. As such, simultaneously running multiple DCD threads on batches of data elements causes result inaccuracy and slow convergence, due to the concurrent updates of multiple coordinates. Some parallelization methods adopt separable approximate functions that depend on the degree of parallelism. Such dependencies result in both poor scalability and slow-convergence. To address these challenges, in this paper we present a new parallel primal-dual algorithm for DCD, called PPD. In PPD, the block data distribution is utilized to obtain a new approximate function that is independent from the parallelism. Moreover, PPD is designed with a novel primal-dual acceleration scheme to approach the optimal solution closely and quickly. We demonstrate the advantages of PPD in terms of scalability and efficiency through experiments. [ABSTRACT FROM AUTHOR]

In this paper, we investigate resource allocation for IRS-assisted green multiuser multiple-input single-output (MISO) systems. To minimize the total transmit power, both the beamforming vectors at the access point (AP) and the phase shifts at multiple IRSs are jointly optimized, while taking into account the minimum required quality-of-service (QoS) of multiple users. First, two novel algorithms, namely a penalty-based alternating minimization (AltMin) algorithm and an inner approximation (IA) algorithm, are developed to tackle the non-convexity of the formulated optimization problem when perfect channel state information (CSI) is available. Existing designs employ semidefinite relaxation in AltMin-based algorithms, which, however, cannot ensure convergence. In contrast, the proposed penalty-based AltMin and IA algorithms are guaranteed to converge to a stationary point and a Karush-Kuhn-Tucker (KKT) solution of the design problem, respectively. Second, the impact of imperfect knowledge of the CSI of the channels between the AP and the users is investigated. To this end, a non-convex robust optimization problem is formulated and the penalty-based AltMin algorithm is extended to obtain a stationary solution. Simulation results reveal a key trade-off between the speed of convergence and the achievable total transmit power for the two proposed algorithms. In addition, we show that the proposed algorithms can significantly reduce the total transmit power at the AP compared to various baseline schemes and that the optimal numbers of transmit antennas and IRS reflecting elements, which maximize the system energy efficiency of the considered system, are finite. [ABSTRACT FROM AUTHOR]

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors. [ABSTRACT FROM AUTHOR]

In this paper, we consider the policy evaluation problem in reinforcement learning with agents on a decentralized and directed network. In order to evaluate the quality of a fixed policy in this decentralized setting, one option is for agents to run decentralized temporal-difference (TD) collaboratively. To account for the practical scenarios where the state and action spaces are large and malicious attacks emerge, we focus on the decentralized TD learning with linear function approximation in the presence of malicious agents (often termed as Byzantine agents). We propose a trimmed mean-based Byzantine-resilient decentralized TD algorithm to perform policy evaluation in this setting. We establish the finite-time convergence rate, as well as the asymptotic learning error that depends on the number of Byzantine agents. Numerical experiments corroborate the robustness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Periodic vehicle routing problem with time windows (PVRPTWs) is an important combinatorial optimization problem that can be applied in different fields. It is essentially a multiobjective optimization problem due to the problem nature. In this paper, a typical multiobjective PVRPTW with five objectives is first defined and new nonsymmetric real-world multiobjective PVRPTW instances are generated. Then, a hybrid multiobjective memetic algorithm is proposed for solving multiobjective PVRPTW. In the proposed algorithm, a two-phase strategy is devised to improve the comprehensive performance in terms of the convergence and diversity. In this strategy, several extreme solutions near an approximate Pareto front (PF) are identified at Phase I, and then the approximate PF is extended at Phase II. The proposed algorithm is extensively tested on both real-world instances and traditional instances. Experiment results show that the proposed algorithm outperforms two representative competitor algorithms on most of the instances. The effectiveness of the two-phase strategy is also confirmed. [ABSTRACT FROM AUTHOR]

The emergence of big data has caused a dramatic shift in the operating regime for optimization algorithms. The performance bottleneck, which used to be computations, is now often communications. Several gradient compression techniques have been proposed to reduce the communication load at the price of a loss in solution accuracy. Recently, it has been shown how compression errors can be compensated for in the optimization algorithm to improve the solution accuracy. Even though convergence guarantees for error-compensated algorithms have been established, there is very limited theoretical support for quantifying the observed improvements in solution accuracy. In this paper, we show that Hessian-aided error compensation, unlike other existing schemes, avoids accumulation of compression errors on quadratic problems. We also present strong convergence guarantees of Hessian-based error compensation for stochastic gradient descent. Our numerical experiments highlight the benefits of Hessian-based error compensation, and demonstrate that similar convergence improvements are attained when only a diagonal Hessian approximation is used. [ABSTRACT FROM AUTHOR]

The matrix decomposing into a sum of low-rank and sparse components has found extensive applications in many areas including video surveillance, computer vision, and medical imaging. In this paper, we propose a new algorithm for recovery of low rank and sparse components of a given matrix. We have also proved the convergence of the proposed algorithm. The simulation results with synthetic and real signals such as image and video signals indicate that the proposed algorithm has a better performance with lower run-time than the conventional methods. [ABSTRACT FROM AUTHOR]

This work addresses the robust principal component analysis (PCA) problem using generalized nonoconvex regularization for low-rank and sparsity promotion. While the popular nuclear and $\ell _1$ -norm penalties have a bias problem, nonconvex regularization can alleviate the bias problem and can be expected to achieve better performance. In this paper, a proximal block coordinate descent (BCD) algorithm is used to efficiently solve the nonconvex regularized robust PCA problem. It is globally convergent under weak conditions. Further, for a popular class of penalties having discontinuous threshoding functions, we establish the convergence to a restricted strictly local minimizer and, also, a local linear convergence rate for the proximal BCD algorithm. Moreover, convergence to a local minimizer has been derived for hard-thresholding. Our result is the first on nonconvex robust PCA with established convergence to strictly local minimizer with local linear convergence rate. Numerical experiments have been provided to demonstrate the performance of the new algorithm. [ABSTRACT FROM AUTHOR]

We propose a fast and scalable polyatomic Frank-Wolfe (P-FW) algorithm for the resolution of high-dimensional LASSO regression problems. This algorithm improves upon traditional Frank-Wolfe methods by considering generalized greedy steps with polyatomic (i.e. linear combinations of multiple atoms) update directions, hence allowing for a more efficient exploration of the search space. To preserve sparsity of the intermediate iterates, we re-optimize the LASSO problem over the set of selected atoms at each iteration. For efficiency reasons, the accuracy of this re-optimization step is relatively low for early iterations and gradually increases with the iteration count. We provide convergence guarantees for our algorithm and validate it in simulated compressed sensing setups. Our experiments reveal that P-FW outperforms state-of-the-art methods in terms of runtime, both for FW methods and optimal first-order proximal gradient methods such as the Fast Iterative Soft-Thresholding Algorithm (FISTA). [ABSTRACT FROM AUTHOR]

Stochastic approximation techniques play an important role in solving many problems encountered in machine learning or adaptive signal processing. In these contexts, the statistics of the data are often unknown a priori or their direct computation is too intensive, and they have thus to be estimated online from the observed signals. For batch optimization of an objective function being the sum of a data fidelity term and a penalization (e.g., a sparsity promoting function), Majorize-Minimize (MM) methods have recently attracted much interest since they are fast, highly flexible, and effective in ensuring convergence. The goal of this paper is to show how these methods can be successfully extended to the case when the data fidelity term corresponds to a least squares criterion and the cost function is replaced by a sequence of stochastic approximations of it. In this context, we propose an online version of an MM subspace algorithm and we study its convergence by using suitable probabilistic tools. Simulation results illustrate the good practical performance of the proposed algorithm associated with a memory gradient subspace, when applied to both nonadaptive and adaptive filter identification problems. [ABSTRACT FROM PUBLISHER]

Ray shooting is a well-studied problem in computer graphics and also has applications in robotics such as collision detection and contact force optimization. Unfortunately, most ray-shooting algorithms developed for graphics applications only allow 3-dimensional (3-D) objects represented as triangle meshes, and therefore are not suited for objects with parametric surfaces or general convex sets in high-dimensional space which robotics applications often require. In contact force optimization, for example, the problem is in the 6-dimensional (6-D) wrench space and it is desirable to consider the nonlinear friction cone without approximating it by a pyramid. This paper discusses existing and novel geometry-based ray-shooting algorithms applicable to general convex sets, and compares their performances in two robotics applications: computing the distance between two convex objects and optimizing contact forces in grasping. [ABSTRACT FROM AUTHOR]

The capacity of noisy quantum channels characterizes the highest rate at which information can be reliably transmitted and it is therefore of practical as well as fundamental importance. Capacities of classical channels are computed using alternating optimization schemes, called Blahut-Arimoto algorithms. In this work, we generalize classical Blahut-Arimoto algorithms to the quantum setting. In particular, we give efficient iterative schemes to compute the capacity of channels with classical input and quantum output, the quantum capacity of less noisy channels, the thermodynamic capacity of quantum channels, as well as the entanglement-assisted capacity of quantum channels. We give rigorous a priori and a posteriori bounds on the estimation error by employing quantum entropy inequalities and demonstrate fast convergence of our algorithms in numerical experiments. [ABSTRACT FROM AUTHOR]

In this article, a new hypervolume-based evolutionary multiobjective optimization algorithm (EMOA), namely, R2HCA-EMOA (R2-based hypervolume contribution approximation EMOA), is proposed for many-objective optimization. The core idea of the algorithm is to use an R2 indicator variant to approximate the hypervolume contribution. The basic framework of the proposed algorithm is the same as SMS-EMOA. In order to make the algorithm computationally efficient, a utility tensor structure is introduced for the calculation of the R2 indicator variant. Moreover, a normalization mechanism is incorporated into R2HCA-EMOA to enhance the performance of the algorithm. Through experimental studies, R2HCA-EMOA is compared with three hypervolume-based EMOAs and several other state-of-the-art EMOAs on 5-, 10-, and 15-objective DTLZ, WFG problems, and their minus versions. Our results show that R2HCA-EMOA is more efficient than the other hypervolume-based EMOAs, and is superior to all the compared state-of-the-art EMOAs. [ABSTRACT FROM AUTHOR]

Proper patrol route planning increases the effectiveness of police patrolling and improves public security. In this paper, we present a new approach for real-time patrol route planning in dynamic environments. We first build a mathematical formulation for the patrol route planning problem under a single patrol unit setting and then propose a fast algorithm developed from the cross entropy (CE) method to meet the real-time computation requirements needed for practical applications. We next generalized the result to the patrol team case. Since the size of feasible team routes grows exponentially as the number of patrol units increases, we propose an approximate CE (ACE) algorithm that balances convergence time with optimality. Compared with the CE algorithm, the ACE algorithm can reduce the convergence time by as much as 48.9% with a less than 1% performance loss. [ABSTRACT FROM PUBLISHER]

We study the properties of the Frank–Wolfe algorithm to solve the m-Exact-Sparse reconstruction problem, where a signal $y$ must be expressed as a sparse linear combination of a predefined set of atoms, called dictionary. We prove that when the signal is sparse enough with respect to the coherence of the dictionary, then the iterative process implemented by the Frank–Wolfe algorithm only recruits atoms from the support of the signal, is the smallest set of atoms from the dictionary that allows for a perfect reconstruction of $y$. We also prove that under this same condition, there exists an iteration beyond which the algorithm converges exponentially. [ABSTRACT FROM AUTHOR]

Recent applications of model-based iterative reconstruction (MBIR) algorithms to multislice helical CT reconstructions have shown that MBIR can greatly improve image quality by increasing resolution as well as reducing noise and some artifacts. However, high computational cost and long reconstruction times remain as a barrier to the use of MBIR in practical applications. Among the various iterative methods that have been studied for MBIR, iterative coordinate descent (ICD) has been found to have relatively low overall computational requirements due to its fast convergence. This paper presents a fast model-based iterative reconstruction algorithm using spatially nonhomogeneous ICD (NH-ICD) optimization. The NH-ICD algorithm speeds up convergence by focusing computation where it is most needed. The NH-ICD algorithm has a mechanism that adaptively selects voxels for update. First, a voxel selection criterion VSC determines the voxels in greatest need of update. Then a voxel selection algorithm VSA selects the order of successive voxel updates based upon the need for repeated updates of some locations, while retaining characteristics for global convergence. In order to speed up each voxel update, we also propose a fast 1-D optimization algorithm that uses a quadratic substitute function to upper bound the local 1-D objective function, so that a closed form solution can be obtained rather than using a computationally expensive line search algorithm. We examine the performance of the proposed algorithm using several clinical data sets of various anatomy. The experimental results show that the proposed method accelerates the reconstructions by roughly a factor of three on average for typical 3-D multislice geometries. [ABSTRACT FROM AUTHOR]

We introduce the decentralized Broyden–Fletcher–Goldfarb–Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. Decentralized quasi-Newton methods are of interest in problems that are not well conditioned, making first-order decentralized methods ineffective, and in which second-order information is not readily available, making second-order decentralized methods impossible. D-BFGS is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition. We additionally provide a formulation of the algorithm in asynchronous settings. Convergence of D-BFGS is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to existing methods are shown numerically. [ABSTRACT FROM PUBLISHER]

A novel design approach is proposed for point-to-point iterative learning control (ILC), enabling system constraints to be satisfied while simultaneously addressing the requirement for high-performance tracking. It is shown that point-to-point ILC design can be formulated and solved using a successive projection first proposed by J. von Neumann, allowing a number of new point-to-point ILC algorithms to be developed and analyzed. To illustrate this framework, two new algorithms are derived with different convergence and computational properties for the constrained point-to-point ILC design problem. The proposed algorithms are validated on a robotic arm with experimental results demonstrating their effectiveness. [ABSTRACT FROM PUBLISHER]

We present two efficient discrete parameter simulation optimization (DPSO) algorithms for the long-run average cost objective. One of these algorithms uses the smoothed functional approximation (SFA) procedure, while the other is based on simultaneous perturbation stochastic approximation (SPSA). The use of SFA for DPSO had not been proposed previously in the literature. Further, both algorithms adopt an interesting technique of random projections that we present here for the first time. We give a proof of convergence of our algorithms. Next, we present detailed numerical experiments on a problem of admission control with dependent service times. We consider two different settings involving parameter sets that have moderate and large sizes, respectively. On the first setting, we also show performance comparisons with the well-studied optimal computing budget allocation (OCBA) algorithm and also the equal allocation algorithm. [ABSTRACT FROM AUTHOR]

We propose a new fast algorithm for solving one of the standard formulations of image restoration and reconstruction which consists of an unconstrained optimization problem where the objective includes an l2 data-fidelity term and a nonsmooth regularizer. This formulation allows both wavelet-based (with orthogonal or frame-based representations) regularization or total-variation regularization. Our approach is based on a variable splitting to obtain an equivalent constrained optimization formulation, which is then addressed with an augmented Lagrangian method. The proposed algorithm is an instance of the so-called alternating direction method of multipliers, for which convergence has been proved. Experiments on a set of image restoration and reconstruction benchmark problems show that the proposed algorithm is faster than the current state of the art methods. [ABSTRACT FROM AUTHOR]