A Temporal Decentralized Algorithm for Optimal Stochastic Energy Scheduling in Microgrids

In Content-Centric Networking (CCN), most existing works do not consider energy savings by turning off network devices in CCN. In this paper, we systematically analyze the energy efficiency problem in CCN by turning off the content routers and network links. We formulate the energy consumption issue as a Mixed Integer Linear Programming (MILP) model, and propose a centralized solution via spanning tree heuristic and a fully distributed consensus optimization algorithm via the alternating direction method of multipliers (ADMM) to solve the problem for CCN. By duplicating flow variables, the energy consumption problem decomposes into node specific subproblems with local variables. These variables are iteratively driven into consensus via the ADMM. Simulation results reveal that the proposed distributed algorithm is amenable to energy-efficient implementation, due to smaller amount of local information exchange at each iteration. Moreover, the proposed algorithm can converge to final status in a significantly smaller number of iterations compared to the method based on dual decomposition. In addition, our algorithm scales better to large networks and it does not require intensive finetuning of the step size.

Model predictive control problems for constrained hybrid systems are usually cast as mixed-integer optimization problems (MIP). However, commercial MIP solvers are designed to run on desktop computing platforms and are not suited for embedded applications which are typically restricted by limited computational power and memory. To alleviate these restrictions, we develop a novel low-complexity, iterative method for a class of non-convex, non-smooth optimization problems. This class of problems encompasses hybrid model predictive control problems where the dynamics are piece-wise affine (PWA). We give conditions such that the proposed algorithm has fixed points and show that, under practical assumptions, our method is guaranteed to converge locally to local minima. This is in contrast to other low-complexity methods in the literature, such as the non-convex alternating directions method of multipliers (ADMM), for which no such guarantees are known for this class of problems. By interpreting the PWA dynamics as a union of polyhedra we can exploit the problem structure and develop an algorithm based on operator splitting procedures. Our algorithm departs from the traditional MIP formulation, and leads to a simple, embeddable method that only requires matrix-vector multiplications and small-scale projections onto polyhedra. We illustrate the efficacy of the method on two numerical examples, achieving good closed-loop performance with computational times several orders of magnitude smaller compared to state-of-the-art MIP solvers. Moreover, it is competitive with ADMM in terms of suboptimality and computation time, but additionally provides local optimality and local convergence guarantees.

In this work, we consider the asynchronous distributed optimization problem in which each node has its own convex cost function and can communicate directly only with its neighbors, as determined by a directed communication topology (directed graph or digraph). First, we reformulate the optimization problem so that Alternating Direction Method of Multipliers (ADMM) can be utilized. Then, we propose an algorithm, herein called Asynchronous Approximate Distributed Alternating Direction Method of Multipliers (AsyAD-ADMM), using finite-time asynchronous approximate ratio consensus, to solve the multi-node convex optimization problem, in which every node performs iterative computations and exchanges information with its neighbors asynchronously. More specifically, at every iteration of AsyAD-ADMM, each node solves a local convex optimization problem for the one of the primal variables and utilizes a finite-time asynchronous approximate consensus protocol to obtain the value of the other variable which is close to the optimal value, since the cost function for the second primal variable is not decomposable. If the individual cost functions are convex, but not-necessarily differentiable, the proposed algorithm converges at a rate of O(1/k), where k is the iteration counter. The efficacy of AsyAD-ADMM is exemplified via a proof-of-concept distributed least square optimization problem with different performance-influencing factors investigated.

This paper discusses about a sparsity based algorithm used for Hyperspectral Image (HSI) classification where the test pixel vectors are sparsely represented as the linear combination of a few number of training samples from a well-organised dictionary matrix. The sparse vector is obtained using Basis Pursuit (BP) which is a constrained l4 minimization problem. This problem is solved by using a simple and powerful iterative algorithm known as Alternating Direction Method of Multipliers (ADMM) which significantly reduces the computational complexity of the problem and thereby speeds up the convergence. The classification accuracy is considerably improved by including efficient preprocessing techniques to remove the unwanted information (noise) present in Hyperspectral images. This paper uses a fast and reliable denoising technique based on Legendre Fenchel Transformation (LFT) to effectively denoise each band of HSI prior to ADMM based classification (proposed method). A comparison of proposed technique with one of the convex optimization tools namely, CVX is given to exhibit the fast convergence of the former method. The experiment is performed on standard Indian Pines dataset captured using AVIRIS sensor. The potential of the proposed method is illustrated by analyzing the classification indices obtained with and without applying any preprocessing methods. With only 10% training set, an overall accuracy of 96.76% is obtained for the proposed method at a much faster rate compared to computation time taken by CVX solver.

The proximal term plays a significant role in the literature of proximal Alternating Direction Method of Multipliers (ADMM), since (positive-definite or indefinite) proximal terms can promote convergence of ADMM and further simplify the involved subproblems. However, an overlarge proximal parameter decelerates the convergence numerically, though the convergence can be established with it. In this paper, we thus focus on a Linearized Symmetric ADMM (LSADMM) with proper proximal terms for solving a family of multi-block separable convex minimization models, and we determine an optimal (smallest) value of the proximal parameter while convergence of this LSADMM can be still ensured. Our LSADMM partitions the data into two group variables and updates the Lagrange multiplier twice in different forms with suitable step sizes. The region of the proximal parameter, involved in the second group subproblems, is partitioned into the union of three different sets. We show the global convergence and sublinear ergodic convergence rate of LSADMM for the two cases, while a counter-example is given to illustrate that convergence of LSADMM can not be guaranteed for the remaining case. Theoretically, we obtain the optimal lower bound of the proximal parameter. Numerical experiments on the so-called latent variable Gaussian graphical model selection problems are presented to demonstrate performance of the proposed algorithm and the significant advantage of the optimal lower bound of the proximal parameter.

Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the alternating direction method of multipliers (ADMM) when inter-agent communications are subject to finite capacity and other practical constraints. While existing quantized ADMM approaches only work for quadratic local objectives, the proposed algorithm can deal with more general objective functions (possibly non-smooth) including the LASSO. Under certain convexity assumptions, our algorithm converges to a consensus within $\log_{1+\eta}\Omega$ iterations, where $\eta>0$ depends on the local objectives and the network topology, and $\Omega$ is a polynomial determined by the quantization resolution, the distance between initial and optimal variable values, the local objective functions and the network topology. A tight upper bound on the consensus error is also obtained which does not depend on the size of the network.

We consider the problem of finding optimal time-periodic sensor schedules for estimating the state of discrete-time dynamical systems. We assume that multiple sensors have been deployed and that the sensors are subject to resource constraints, which limits the number of times each can be activated over one period of the periodic schedule. We seek an algorithm that strikes a balance between estimation accuracy and total sensor activations over one period. We make a correspondence between active sensors and the nonzero columns of the estimator gain. We formulate an optimization problem in which we minimize the trace of the error covariance with respect to the estimator gain while simultaneously penalizing the number of nonzero columns of the estimator gain. This optimization problem is combinatorial in nature, and we employ the alternating direction method of multipliers (ADMM) to find its locally optimal solutions. Numerical results and comparisons with other sensor scheduling algorithms in the literature are provided to illustrate the effectiveness of our proposed method.

This paper proposes a nonlinear weighted anisotropic total variation (NWATV) regularization technique for electrical impedance tomography (EIT). The key idea is to incorporate the internal inhomogeneity information (e.g., edges of the detected objects) into the EIT reconstruction process, aiming to preserve the conductivity profiles (to be detected). We study the NWATV image reconstruction by employing a novel soft thresholding based reformulation included in the alternating direction method of multipliers (ADMM). To evaluate the proposed approach, numerical simulations and human EIT lung imaging are carried out. It is demonstrated that the properties of the internal inhomogeneity are well preserved and improved with the proposed regularization approach, in comparison to traditional total variation (TV) and recently proposed fidelity embedded regularization approaches. Owing to the simplicity of the proposed method, the computational cost is significantly decreased compared with the well established primal-dual algorithm. Precisely, with the proposed algorithm, we are able to alleviate the staircase effect arising in TV regularization and improve the reconstruction accuracy for FER does. To achieve similar accuracy as TV does, the computational times are reduced from 2.311s to 0.629s and 1.733s to 0.428s in 2D and 3D simulations, respectively, and the computational time is reduced from greater than 2s to less than 0.2s in the human experiment. Meanwhile, it was found that the proposed regularization method is quite robust to the measurement noise, which is one of the main uncertainties in EIT.

Mobile edge computing is a promising framework for mobile virtual reality (VR) game. Although there are several existing studies on the edge assisted mobile VR game system, they lack the consideration of provisioning services with satisfactory QoE to a large number of users. In this paper, we consider the problem of providing QoE-oriented edge assisted mobile VR game as a service to multiple users, with a comprehensive QoE concern of both visual and delay aspects. Due to the unique features of mobile VR game, the problem is formulated into a Mixed Integer Quadratically Constrained Quadratic Programming (MIQCQP) problem. We show that the problem is NP-hard with object placement decision and rendering level selection decision quadratically coupling together. To solve this problem, we propose the Alternating Directions Method of Multipliers (ADMM) algorithm which can iteratively decouple the quadratic terms and reform the problem into the efficiently solvable MIQCQP-1 (i.e., MIQCQP with one constraint) problem. Trace driven simulation shows that our algorithm fits the edge assisted mobile VR game scenario well with fast computation time (at least 4 orders of magnitude less computation time compared to Gurobi solver) and good performance (at least 18% of user visual QoE improvement compared to other mobile VR scheme).

Rate Splitting (RS) is a versatile and powerful technique for multi-antenna transmission. In this paper, we study the precoding optimization for RS, which is critically important for improving the system performance but often challenging to address. We first investigate the non-convex sum rate maximization problem under perfect Channel State Information at the Transmitter (CSIT). By constructing a separable structure for the sum-of-functions-of-ratios problem and jointly leveraging the Convex Concave Procedure (CCP) and the Alternating Direction Method of Multipliers (ADMM), we obtain a fast algorithm that substantially reduces the overall computational time through the parallel computation and explicit closed-form solutions. We then investigate the average sum rate maximization problem under imperfect CSIT, which is known as a more challenging non-convex stochastic problem. To obtain a fast algorithm for practical use, we carefully approximate the non-convex stochastic problem to a non-convex deterministic one with acceptable performance loss and tailor the fast algorithm derived from perfect CSIT for imperfect CSIT with modest changes. Numerical results show that compared to the state-of-the-art algorithms, the proposed algorithms achieve comparable sum rates or average sum rates but short computation times for large problem sizes, owing to the unique parallel computation structures and few matrix inverse operations.

In model predictive control, the control action is found at each sampling time by solving an online optimization problem. Computationally, this step is very demanding, especially if compared to the evaluation of traditional control laws. This has limited the application of model predictive control to systems with slow dynamics for many years. Recently, several methods have been proposed in the literature which promise a substantial reduction of the computation time by either running the computation in parallel (distributed model predictive control) or exploiting the problem structure (fast model predictive control). A combination of these methods has not yet been considered in the literature. To achieve this goal, different optimization techniques need to be employed at once. The order of how these methods are applied matters. This paper considers fast distributed model predictive control combining the alternating direction method of multipliers (ADMM), the interior point method (IPM) and the Riccati iteration for a particular class of multi-agent systems for which the order of the methods can be arbitrarily changed. This leads to two different solver schemes where a trade-off arises between computation time and number of communications required to reach consensus. A simplified problem involving the formation control of a fleet of vehicles is considered at the end.

A new dissimilarity-weighted sparse self-representation (DWSSR) method has been presented to select a proper band subset for hyperspectral imagery (HSI) classification. The DWSSR assumes that all the bands can be represented by the selected band subset, and it formulates sparse representation of all the bands into a sparse self-representation (SSR) model with row-sparsity constraint in the coefficient matrix. Furthermore, the DWSSR integrates a dissimilarity-weighted regularization term with the SSR model to avoid the issue of too-close bands encountered in the SSR. The regularization term explains the encoding cost of all bands with the representative bands, and a new composite dissimilarity measure which combines spectral information divergence with intraband correlation is implemented to estimate the encoding weight. The DWSSR program is solved by the alternating direction method of multipliers (ADMM) framework, and the representative bands are finally selected according to the norm rankings of nonzero rows in the estimated coefficient matrix. Five groups of experiments on three popular HSI datasets are designed to test the performance of DWSSR in band selection, and five state-of-the-art methods are utilized to make comparisons. The results show that the DWSSR performs almost best among all the six methods, either in computational time or classification accuracies.

Model Predictive Control (MPC) is a highly effective control method with drawbacks. The computational overhead required makes deploying high update rates using embedded controllers problematic. This paper presents a software configurable and parallelized co-processor architecture for an embedded MPC controller that can control the physical processes represented by a linear state-space model on a Field Programmable Gate Array (FPGA) coupled with an ARM Processor. This paper outlines a methodology that bridges the gap between controls and embedded engineers allowing them to work in parallel with well-defined rolls. Our architecture implements an MPC that allows the model unlimited fidelities over multiple non-uniformly spaced optimization horizons and is solved using the division-free algorithm, Alternating Direction Method of Multiplier (ADMM). During runtime, the designer dynamically updates the desired plant trajectory and the system's constraints with the highest-fidelity model over the smallest time step. A combination of hardware (HW) and software (SW) converts each model into the appropriate fidelity and optimization horizons in parallel with the MPC. There is a 4x speed up of a 256 decision variable system running on a Zync-7020 FPGA and ARM Cortex-A9 processor when compared to Operator Splitting Quadratic Program (OSQP) algorithm running on an Intel Xeon E5-2650. This paper showcases the trade-off of computational resources of Block RAM, DSP, and off-chip memory; computation time under various hardware configurations; and controller response of our design operating on a square wave and over rolling hills. Our system performance is within 10\% of other floating point ADMM-based FPGA accelerators that are not able to use unlimited multifidelity models, non-uniformly spaced prediction horizons, switch out scenarios, and the ability to update course trajectory, and maximum and minimum constraints while in operation.

Multistage stochastic programs are effective for solving long-term planning problems under uncertainty. Such programs are usually based on a scenario model of future environment developments. A good approximation of the underlying stochastic process may involve a very large number of scenarios and their probabilities. We discuss the case when enough data paths can be generated, but due to solvability of stochastic program the scenario tree has to be constructed. The proposed strategy is to generate the multistage scenario tree from the set of individual scenarios by bundling scenarios based on cluster analysis. The K-means clustering approach is modified to capture the interstage dependencies in order to model the sequential decisions. The described scenario tree generation method is implemented on sampled data of nominal interest rate.

With the insignificant incremental cost involved in hydrogeneration, the problem of minimizing the operation cost of a hydro-thermal system essentially reduces to that of minimizing the fuel cost for thermal plants under the constraints of the water available for hydro generation in a given period of time. The problem thus belongs to the realm of dynamic optimization.In the past, many papers pertaining to optimal hydro-thermal scheduling assume water inflows to reservoirs and load demand to be deterministic. In practice, however, this is not true. To be realistic, the scheduling problem must be tackled through stochastic optimization. This paper presents a new effective approach to the optimal stochastic hydro-thermal scheduling problem. A computational algorithm based on first- order gradient technique is developed to solve the scheduling problem.