Active Set Method Research Articles

Statistical Method Based Waveform Optimization in Collocated MIMO Radar Systems

Multiple-input multiple-output (MIMO) radar has acquired considerable attention as it offers an additional degree of freedom which results in performance gains when contrasted with the regular single antenna element radar system. Waveform optimization in MIMO radar is essential as it can offer tremendous improvements in target detection which are quantified in terms of reductions in the symbol error rate and improvements in target detection probability. In this work, we foster a strategy for the optimization of transmitter and receiver waveform in a collocated MIMO radar by only considering the second order statistics, thus relaxing the information of the instantaneous target states. Our contributions are primarily two-fold. First, we find a closed-form expression of the outage probability of an unknown target under clutter environment. For this prospect, we model the signal-to-interference-plus-noise ratio in a canonical quadratic structure, and then utilize the modern residue theory approach to characterize the distribution function. Secondly, we propose constrained and unconstrained optimization problems for the reduction in outage probability using algorithmic techniques such as interior-point, sequential-quadratic programming, and the active-set method for the optimization of the transmitter and receiver waveform. We also provide simulated re-enactments to validate our hypothetical deductions.

A dual active set method for <inline-formula><tex-math id="M1">$ \ell $</tex-math></inline-formula>1-regularized problem

We consider an $ \ell $1-regularized problem, which has many applications such as compressed sensing, MRI, and seismic images. Although there have been some methods for the problem, they cannot obtain a highly accurate solution. To overcome this drawback, we propose a dual active set method, which is an active set method for the Fenchel dual problem of the $ \ell $1-regularized problem. Our method finds a highly accurate solution quickly because of the following features of the dual problem: (i) the dimension of the decision variables is smaller; (ii) since the optimal solution of the primal problem is sparse, the active constraints of the optimal solution of the dual problem are few and can be identified quickly. Then, we show that the method outputs the solution with finite iterations when it solves certain subproblems exactly. Moreover, we give its efficient and concrete implementation for Basis Pursuit Denoising (BPDN), which is a typical $ \ell $1-regularized problem. In numerical experiments for BPDN, our method provides more accurate solutions than all baselines in comparable computing time.

Semantic Segmentation of Fish and Underwater Environments Using Deep Convolutional Neural Networks and Learned Active Contours

The conservation of marine resources requires constant monitoring of the underwater environment by researchers. For this purpose, visual automated monitoring systems are of great interest, especially those that can describe the environment using semantic segmentation based on deep learning. Although they have been successfully used in several applications, such as biomedical ones, obtaining optimal results in underwater environments is still a challenge due to the heterogeneity of water and lighting conditions, and the scarcity of labeled datasets. Even more, the existing deep learning techniques oriented to semantic segmentation only provide low resolution results, lacking the enough spatial details for a high performance monitoring. To address these challenges, a combined loss function based on the active contour theory and level set methods is proposed to refine the spatial segmentation resolution and quality. To evaluate the method, a new underwater dataset with pixel annotations for three classes (fish, seafloor, and water) was created using images from publicly accessible datasets like SUIM, RockFish, and DeepFish. The performance of architectures of convolutional neural networks (CNNs), such as UNet and DeepLabV3+, trained with different loss functions (cross entropy, dice, and active contours) was compared, finding that the proposed combined loss function improved the segmentation results by around 3%, both in the metric Intercept Over Union (IoU) as in Hausdorff Distance (HD).

Primal-Dual Active-Set Method for the Valuation of American Exchange Options

Primal-Dual Active-Set Method for the Valuation of American Exchange Options

Experiments with Active-Set LP Algorithms Allowing Basis Deficiency

An interesting question for linear programming (LP) algorithms is how to deal with solutions in which the number of nonzero variables is less than the number of rows of the matrix in standard form. An approach is that of basis deficiency-allowing (BDA) simplex variations, which work with a subset of independent columns of the coefficient matrix in standard form, wherein the basis is not necessarily represented by a square matrix. We describe one such algorithm with several variants. The research question deals with studying the computational behaviour by using small, extreme cases. For these instances, we must wonder which parameter setting or variants are more appropriate. We compare the setting of two nonsimplex active-set methods with Holmström’s TomLab LpSimplex v3.0 commercial sparse primal simplex commercial implementation. All of them update a sparse QR factorization in Matlab. The first two implementations require fewer iterations and provide better solution quality and running time.

ElastoMonolith

Simultaneous coupling of diverse physical systems poses significant computational challenges in terms of speed, quality, and stability. Rather than treating all components with a single discretization methodology (e.g., smoothed particles, material point method, Eulerian grid, etc.) that is ill-suited to some components, our solver, ElastoMonolith , addresses three-way interactions among standard particle-in-cell-based viscous and inviscid fluids, Lagrangian mesh-based deformable bodies, and rigid bodies. While prior methods often treat some terms explicitly or in a decoupled fashion for efficiency, often at the cost of robustness or stability, we demonstrate the effectiveness of a strong coupling approach that expresses all of the relevant physics within one consistent and unified optimization problem, including fluid pressure and viscosity, elasticity of the deformables, frictional solid-solid contact, and solid-fluid interface conditions. We further develop a numerical solver to tackle this difficult optimization problem, incorporating projected Newton, an active set method, and a transformation of the inner linear system matrix to ensure symmetric positive definiteness. Our experimental evaluations show that our framework can achieve high quality coupling results that avoid artifacts such as volume loss, instability, sticky contacts, and spurious interpenetrations.

Unified primal-dual active set method for dynamic frictional contact problems

In this paper, we propose a semi-smooth Newton method and a primal-dual active set strategy to solve dynamical contact problems with friction. The conditions of contact with Coulomb’s friction can be formulated in the form of a fixed point problem related to a quasi-optimization one thanks to the semi-smooth Newton method. This method is based on the use of the primal-dual active set (PDAS) strategy. The main idea here is to find the correct subset mathcal{A} of nodes that are in contact (active) opposed to those which are not in contact (inactive). For each case, the nonlinear boundary condition is replaced by a suitable linear one. Numerical experiments on both hyper-elastic problems and rigid granular materials are presented to show the efficiency of the proposed method.

Optimization of hydraulic power take-off system settings for point absorber wave energy converter

Ocean wave renewable energy is becoming a key part of the renewable energy industry over the recent decades. By developing wave energy converters (WECs), their power take-off (PTO) systems have been investigated to enhance the power extraction from the ocean. Adjusting PTO parameters is a challenging optimization problem because there is a complex and nonlinear relationship between these parameters and the absorbed power output. In this regard, this study aims to optimize the PTO system parameters of a point absorber wave energy converter in the wave data-set in Perth, on the Western Australian coasts. The converter is numerically designed to oscillate against irregular and multi-dimensional waves and sensitivity analysis for PTO settings. Then, to find the optimal PTO system parameters which lead to the highest power output, ten optimization approaches are incorporated to solve the nonlinear problem, including the Nelder-Mead search method, Active-set method, Sequential quadratic Programming method (SQP), Multi-Verse Optimizer (MVO), and six modified combination of Genetic, Surrogate and fminsearch techniques. After a feasibility landscape analysis, the optimization outcome is carried out and gives us the best answer in terms of PTO system settings. Finally, the investigation shows that the modified combinations of Genetic, Surrogate, and fminsearch approaches can outperform the others in the selected wave scenario, as well as with regard to the interaction between PTO system variables.

A Unifying Complexity Certification Framework for Active-Set Methods for Convex Quadratic Programming

In model-predictive control (MPC), an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these efficiently and to have good upper bounds on worst-case solution time. Often for linear MPC problems, the optimization problem in question is a quadratic program (QP) that depends on parameters such as system states and reference signals. A popular class of methods for solving such QPs is active-set methods, where a sequence of linear systems of equations is solved. We propose an algorithm for computing which sequence of subproblems an active-set algorithm will solve, for every parameter of interest. These sequences can be used to set worst-case bounds on how many iterations, floating-point operations, and, ultimately, the maximum solution time the active-set algorithm requires to converge. The usefulness of the proposed method is illustrated on a set of QPs originating from MPC problems, by computing the exact worst-case number of iterations primal and dual active-set algorithms require to reach optimality.

Low probability of intercept‐based cooperative node selection and transmit resource allocation for multi‐target tracking in multiple radars architecture

A low probability of intercept (LPI)-based cooperative node selection and transmit resource allocation (CNS-TRA) strategy is proposed for multi-target tracking in multiple radars architecture (MRA). The key idea of the proposed CNS-TRA strategy is to coordinate the radar node selection and the transmit resource that is, dwell time, transmit power, and effective bandwidth allocation to improve the LPI performance, under the constraints of predefined target tracking accuracy requirement and several resource budgets. By incorporating the above controllable parameters, the Bayesian Cramér-Rao lower bound is calculated and used as the accuracy metric for target tracking. Subsequently, this paper develops a fast and effective two-stage-based solution methodology to solve the resulting non-convex and non-linear optimisation problem. Specifically, the optimisation problem can be decomposed into two sub-problems, that is, the radar node selection sub-problem and the transmit resource allocation sub-problem. The active-set method and the interior point approach are utilised to solve those two sub-problems, respectively. Simulation results demonstrate that the CNS-TRA strategy has superiority over other existing algorithms and can achieve better LPI performance for MRA.

Unknown Transmit Power RSSD-Based Localization in a Gaussian Mixture Channel

Localization is a critical task in wireless sensor networks (WSNs). However, accurate localization is difficult when there is noise from external sources and faulty nodes, especially when the transmit power is unknown. Signal strength-based localization methods are popular due to their low complexity and simple implementation. In this paper, robust localization based on the received signal strength difference (RSSD) is considered with unknown transmit power and Gaussian mixture noise in the presence of faulty nodes. A robust fault-tolerant localization (RFLT) technique is proposed by reformulating the original localization problem using a generalized trust-region subproblem (GTRS) framework. The resulting problem is non-convex so it is divided into two subproblems using a regularization item (RI) with a block-update surrogate function (BUSF). The active set method (ASM) is used to obtain an initial solution. The corresponding Cramer–Rao lower bound (CRLB) for Gaussian mixture noise is derived as a benchmark. Simulation results are presented which show that the performance of the proposed method is superior to other state-of-the-art methods.

An efficient bounded-variable nonlinear least-squares algorithm for embedded MPC

This paper presents a novel approach to solve linear and nonlinear model predictive control (MPC) problems that requires small memory footprint and throughput and is particularly suitable when the model and/or controller parameters change at runtime. The contributions of the paper include: (i) a formulation of the nonlinear MPC problem as a bounded-variable nonlinear least-squares (BVNLS) problem, demonstrating that the use of an appropriate solver can outperform industry-standard solvers; (ii) an easily-implementable library-free BVNLS solver with a novel proof of global convergence; (iii) a matrix-free method for computing the products of vectors and Jacobians, required by BVNLS; (iv) an efficient method for updating sparse QR factors when using active-set methods to solve sparse BVNLS problems. Thanks to explicitly parameterizing the optimization algorithm in terms of the model and MPC tuning parameters, the resulting approach is inherently and immediately adaptive to any changes in the MPC formulation. The same algorithmic framework can cope with linear, nonlinear, and adaptive MPC variants based on a broad class of prediction models and sum-of-squares cost functions.

A compendium of optimization algorithms for distributed linear-quadratic MPC

Abstract Model Predictive Control (MPC) for {networked, cyber-physical, multi-agent} systems requires numerical methods to solve optimal control problems while meeting communication and real-time requirements. This paper presents an introduction on six distributed optimization algorithms and compares their properties in the context of distributed MPC for linear systems with convex quadratic objectives and polytopic constraints. In particular, dual decomposition, the alternating direction method of multipliers, a distributed active set method, an essentially decentralized interior point method, and Jacobi iterations are discussed. Numerical examples illustrate the challenges, the prospect, and the limits of distributed MPC with inexact solutions.

Comparing alternative PDA solvers with EPANET

Abstract This work compares several alternative methods of pressure-driven analysis (PDA) implemented within the code base of the EPANET water distribution system modeling software. The resulting code includes a direct method, the original and a newly modified version of the inverse method currently used by EPANET 2.2, and two recently published methods (the global gradient approach-based PDA and the active set method). The latter four methods solve PDA problems using an inverse flow–pressure relationship, whereas the direct method uses the original relationship. The alternative methods were extensively tested, and their performance was compared over several case study water distribution networks of vastly different sizes and complexities. The results showed that all of the new inverse methods are equally efficient and reliable, whereas the direct method is less reliable by having a higher frequency of failing to converge.

Design and Implementation of Model Predictive Controller

The precise position control of a DC servo motor is a major concern in today's control theory. This work presents position following and forecast of DC servo engine utilizing an alternate control technique. Control technique is required to limit and diminish the consistent state error. A model predictive controller MPC is utilized to plan and actualize these prerequisites. Two sorts of controlling techniques are presented in this task. The Active Set Method (ASM), the inside point technique (IIP), and have been utilized as controlling strategies. This work distinguishes and depicts the plan decisions identified with a two sorts of controllers and judicious regulator for a DC servo motor. Execution of these regulators has been confirmed through reproduction utilizing MATLAB/SIMULINK programming. As indicated by the recreation results the Comparisons among ASM, IIP. The tuning strategy was increasingly proficient in improving the progression reaction attributes, for example, decreasing the rise time, settling time and most prominent overshoot in Position control of DC servo motor.

A Neuro-Evolution Heuristic Using Active-Set Techniques to Solve a Novel Nonlinear Singular Prediction Differential Model

In this study, a novel design of a second kind of nonlinear Lane–Emden prediction differential singular model (NLE-PDSM) is presented. The numerical solutions of this model were investigated via a neuro-evolution computing intelligent solver using artificial neural networks (ANNs) optimized by global and local search genetic algorithms (GAs) and the active-set method (ASM), i.e., ANN-GAASM. The novel NLE-PDSM was derived from the standard LE and the PDSM along with the details of singular points, prediction terms and shape factors. The modeling strength of ANN was implemented to create a merit function based on the second kind of NLE-PDSM using the mean squared error, and optimization was performed through the GAASM. The corroboration, validation and excellence of the ANN-GAASM for three distinct problems were established through relative studies from exact solutions on the basis of stability, convergence and robustness. Furthermore, explanations through statistical investigations confirmed the worth of the proposed scheme.

An Interior Point Method Applied to Flow Constraints in a Pressure-Dependent Water Distribution System

This paper used the fusion of an active-set method (ASM) and an interior point method (IPM), with a Newton method, to solve for the steady-state flows, heads, and outflows of a pressure-dependent water distribution system. The outflow constraints which arise from the pressure dependency are handled by an ASM, and the linkflow constraints are handled by an IPM. The authors believe that this is the first time an ASM and an IPM have been used together in this way to solve a real-world optimization problem. Including flow constraints in a network model allows a variety of flow control devices (flow control valves, check valves, pumps) to be modeled efficiently. The new method does not require damping. The separate treatment methods for the two constraint sets mean that the linear inequality constraint qualification condition cannot be violated during iteration, unlike the case in which all the constraints are handled by an ASM. The method was shown to converge quickly on nine case study networks, the largest of which had more than 157,000 links, 150,000 nodes, and 6,000 linkflow constraints. When tested on those same nine networks, an interior point optimizer software package took about 2–4 times longer than the new method for five of the networks, 7 and 9 times as long for two of the networks, and about an equal amount of time for the remaining two networks. For the largest network, the software package took 34 min, whereas the method presented here took 4 min. The generality of the method makes it applicable to network design and management, capacity analysis, and self-cleaning networks.

Support solving method for box-constrained indefinite quadratic minimisation problems

This paper provides a new support solving method (SSM) of global optimisation for the box-constrained non-convex quadratic minimisation problem, in particular with one negative eigenvalue. We investigate the support of the objective function and exploit properties of the indefinite associated matrix for establishing global optimality criterion (necessary and sufficient conditions). Furthermore, using these conditions and computational techniques of abstract convexity, we suggest an SSM that can effectively solve an indefinite quadratic minimisation problem, providing thus a global minimiser. We present numerical examples and generate some test problems with known global minimiser, solving them by the proposed SSM. Finally, we provide the comparative effectiveness of the SSM with active set method (ASM) and interior point method (IPM) implemented under MATLAB optimisation toolbox.

Discrete-Time Differential Dynamic Programming on SO(3) With Pose Constraints

The motion of many robotics systems, such as the rotation of unmanned aerial vehicles, can be modeled by SO(3). However, the difficulties in the parameterization of the SO(3) makes it hard to implement the state-of-the-art collision avoidance algorithm. In this paper, we present a new method for control on SO(3) via the combination of the nonlinear state constraints and geometric control technique. We first define the nonlinear constraints for trajectory optimization on SO(3). Then we solve the trajectory optimization problem by constrained Differential Dynamic Programming (DDP) in a Riemannian geometry framework. The first and second-order expansion of the cost function and dynamics are derived in a coordinate-free manner. The safety condition represented by nonlinear constraints is incorporated into the DDP via an active set method, where we find the active set in the backward path to obtain the optimal control policy. We validated our methods on motion planning of rigid model on SO(3) manifold where pose constraints are imposed. Our methods outperform the baseline methods in terms of convergence speed and numerical robustness to disturbance. The numerical robustness is essential when the system is initialized far from the local optimum.

Numerical Simulations of Vaccination and Wolbachia on Dengue Transmission Dynamics in the Nonlinear Model

In this study, it is indicated that the world can get rid of the dengue virus by using vaccines and Wolbachia. In many findings, it is observed that Wolbachia therapy is efficacious in those regions that display the minimal to moderate the transmission level. On the contrary, vaccination is highly successful when used in serologically persons and places with large transmission levels. The resilience of stochastic methodology based on the numerical computing schemes will be used to exploit the artificial neural networks (ANNs) modelling legacy, as well as the metaheuristic intelligence using the hybrid of global and local search schemes thru genetic algorithms (GAs) and active-set method (ASA). The combination of both strategies is used to manage the numerical therapies of the mathematical form of the dengue model. The optimal control results through GA-ASA can be retrieved by offering an error-based fitness function generated for dengue model represented via nonlinear systems of equations. The acquired findings are compared to the Adams numerical results to ensure that the suggested stochastic system is accurate. For determining convergence, the training contours are based on various contact rate values. Furthermore, the statistical achievements of the suggested stochastic scheme to solve the novel developed dengue model, which demonstrate the stability and dependability of the dynamical system scheme.