Dual Algorithm Research Articles

Decentralized Algorithms for Wasserstein Barycenters

In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides in two scenarios: (I) the measures are given and we need to compute their Wasserstein barycenter, and (ii) the measures are generated from a probability distribution and we need to calculate the population barycenter of the distribution defined by the notion of Fr\'echet mean. The statistical focus is estimating the sample size of measures necessary to calculate an approximation for Fr\'echet mean (barycenter) of a probability distribution with a given precision. For empirical risk minimization approaches, the question of the regularization is also studied together with proposing a new regularization which contributes to the better complexity bounds in comparison with quadratic regularization. The computational focus is developing algorithms for calculating Wasserstein barycenters: both primal and dual algorithms which can be executed in a decentralized manner. The motivation for dual approaches is closed-forms for the dual formulation of entropy-regularized Wasserstein distances and their derivatives, whereas the primal formulation has closed-form expression only in some cases, e.g., for Gaussian measures. Moreover, the dual oracle returning the gradient of the dual representation for entropy-regularized Wasserstein distance can be computed for a cheaper price in comparison with the primal oracle returning the gradient of the entropy-regularized Wasserstein distance. The number of dual oracle calls, in this case, will also be less, i.e., the square root of the number of primal oracle calls. This explains the successful application of the first-order dual approaches for the Wasserstein barycenter problem.

Sleep-Aware Adaptive Deep Brain Stimulation Control: Chronic Use at Home With Dual Independent Linear Discriminate Detectors.

Adaptive deep brain stimulation (aDBS) is a promising new technology with increasing use in experimental trials to treat a diverse array of indications such as movement disorders (Parkinson’s disease, essential tremor), psychiatric disorders (depression, OCD), chronic pain and epilepsy. In many aDBS trials, a neural biomarker of interest is compared with a predefined threshold and stimulation amplitude is adjusted accordingly. Across indications and implant locations, potential biomarkers are greatly influenced by sleep. Successful chronic embedded adaptive detectors must incorporate a strategy to account for sleep, to avoid unwanted or unexpected algorithm behavior. Here, we show a dual algorithm design with two independent detectors, one used to track sleep state (wake/sleep) and the other used to track parkinsonian motor state (medication-induced fluctuations). Across six hemispheres (four patients) and 47 days, our detector successfully transitioned to sleep mode while patients were sleeping, and resumed motor state tracking when patients were awake. Designing “sleep aware” aDBS algorithms may prove crucial for deployment of clinically effective fully embedded aDBS algorithms.

Q-SR: An extensible optimization framework for segment routing

Segment routing (SR) combines the advantages of source routing powered by software-defined networking (SDN) paradigm and hop-by-hop routing in legacy network infrastructure. The recent applications of SR in multi-domain network and service function chaining (SFC) entail the efficient use of multiple segments. However, because of the computation inefficiency, it is nearly impossible to accurately evaluate whether and to what extent various types of networks will benefit from SR with multiple segments using conventional approaches. In this paper, we propose a flexible Q-SR framework as well as its formulation in order to fully explore the potential of SR from an algorithmic perspective. The framework is highly extensible to design and evaluate algorithms that can be adapted to various network topologies and traffic matrices. For the offline setting, we develop a fully polynomial time approximation scheme (FPTAS) which can find a (1+ω)-approximation solution for any specified ω>0 in time that is a polynomial function of the network size. To the best of our knowledge, the proposed FPTAS is the first algorithm that can compute arbitrarily accurate solution. For the online setting, we develop an online primal–dual algorithm that is proven to be O(1)-competitive and violates link capacities by a factor of O(logn), where n is the node number of the network. For the proposed approximation algorithms, we prove theoretical performance bounds and conduct extensive simulations on synthetic and realistic networks to analyze SR related and algorithmic parameters and validate the computation efficiency in both offline and online scenarios.

Feature Extraction and Recognition of Medical CT Images Based on Mumford-Shah Model

In this paper, we propose an improved algorithm based on the active contour model Mumford-Shah model for CT images, which is the subject of this study. After analyzing the classical Mumford-Shah model and related improvement algorithms, we found that most of the improvement algorithms start from the initialization strategy of the model and the minimum value solution of the energy generalization function, so we will also improve the classical Mumford-Shah model from these two perspectives. For the initialization strategy of the Mumford-Shah model, we propose to first reduce the dimensionality of the image data by the PCA principal component analysis method, and for the reduced image feature vector, we use K -means, a general clustering method, as the initial position algorithm of the segmentation curve. For the image data that have completed the above two preprocessing processes, we then use the Mumford-Shah model for image segmentation. The Mumford-Shah curve evolution model solves the image segmentation by finding the minimum of the energy generalization of its model to obtain the optimal result of image segmentation, so for solving the minimum of the Mumford-Shah model, we first optimize the discrete problem of the energy generalization of the model by the convex relaxation technique and then use the Chambolle-Pock pairwise algorithm We then use the Chambolle-Pock dual algorithm to solve the optimization problem of the model after convex relaxation and finally obtain the image segmentation results. Finally, a comparison with the existing model through many numerical experiments shows that the model proposed in this paper calculates the texture image segmentation with high accuracy and good edge retention. Although the work in this paper is aimed at two-phase image segmentation, it can be easily extended to multiphase segmentation problems.

Low-Speed Vehicle Path-Tracking Algorithm Based on Model Predictive Control Using QPKWIK Solver

Abstract Automated valet parking is a part of autonomous vehicles. Path tracking is a vital capability of autonomous vehicles. In the scenario of automatic valet parking, the existing control algorithm will produce a high tracking error and a high computational burden. This paper proposes a path-tracking algorithm based on model predictive control to adapt to low-speed driving. By using the model predictive control method and vehicle kinematics model, a path tracking controller is designed. Combining the dual algorithm to further optimize the solver, a new quadratic programming (QP) knows what it knows (QPKWIK) solver is proposed. The simulation results show that the solution time of the QPKWIK solver is 25% less than that of the QP solver, and the tracking error is reduced by up to 41% compared with the QP solver. In the parking lot, the tracking performance is tested under four common scenarios, and the experimental results show that this controller has better tracking performance.

An Effective Techniques Using Apriori and Logistic Methods in Cloud Computing

This paper presents a creativity data prefetching scheme on the loading servers in distributed file systems for cloud computing. The server will get and piggybacked the frequent data from the client system, after analyzing the fetched data is forward to the client machine from the server. To place this technique to work, the data about client nodes is piggybacked onto the real client I/O requests, and then forwarded to the relevant storage server. Next, dual prediction algorithms have been proposed to calculation future block access operations for directing what data should be fetched on storage servers in advance. Finally, the prefetching data can be pressed to the relevant client device from the storage server. Over a series of evaluation experiments with a group of application benchmarks, we have demonstrated that our presented initiative prefetching technique can benefit distributed file systems for cloud environments to achieve better I/O performance. In particular, configuration-limited client machines in the cloud are not answerable for predicting I/O access operations, which can certainly contribute to preferable system performance on them.

A crystal symmetry-invariant Kobayashi–Warren–Carter grain boundary model and its implementation using a thresholding algorithm

One of the most important aims of grain boundary modeling is to predict the evolution of a large collection of grains in phenomena such as abnormal grain growth, coupled grain boundary motion, and recrystallization that occur under extreme thermomechanical loads. A unified framework to study the coevolution of grain boundaries with bulk plasticity has recently been developed by [1], which is based on modeling grain boundaries as continuum dislocations governed by an energy based on the Kobayashi–Warren–Carter (KWC) model [2,3]. While the resulting unified model demonstrates coupled grain boundary motion and polygonization (seen in recrystallization), it is restricted to grain boundary energies of the Read–Shockley type, which applies only to small misorientation angles. In addition, the implementation of the unified model using finite elements inherits the computational challenges of the KWC model that originate from the singular diffusive nature of its governing equations. The main goal of this study is to generalize the KWC functional to grain boundary energies beyond the Read–Shockley-type that respect the bicrystallography of grain boundaries. The computational challenges of the KWC model are addressed by developing a thresholding method that relies on a primal dual algorithm and the fast marching method, resulting in an O(NlogN) algorithm, where N is the number of grid points. We validate the model by demonstrating the Herring angle and the von Neumann–Mullins relations, followed by a study of the grain microstructure evolution in a two-dimensional face-centered cubic copper polycrystal with crystal symmetry-invariant grain boundary energy data obtained from the covariance grain boundary model of [4,5].

Analisis dan Implementasi Algoritma Asimetris Dual Modulus RSA (DM-RSA) pada Aplikasi Chat

The RSA algorithm is one of the cryptographic algorithms with an asymmetric model where the algorithm has two keys, namely the public key and the private key. However, as time goes on, these algorithms are increasingly exposed to security holes and make this algorithm vulnerable to being hacked by people who do not have authority. The vulnerability stems from the algorithm's public keys (e and n). The strength of the RSA algorithm is based on the difficulty of factoring two prime numbers that are generated during the key generation process, if these values ​​can be known using certain methods, the public key and private key values ​​will be found. Therefore, there are many studies that improvise the RSA algorithm, one of which is the Dual Modulus RSA (DM-RSA) algorithm. The algorithm uses four prime numbers which produce 2 modulus and 4 keys (2 public keys and 2 private keys). From the results of the Kraitchik factorization test, it was found that the DM-RSA algorithm was proven to be more resistant up to 2 times or even more than the standard RSA algorithm. This is evidenced by the fact that the value of n is 24 bits, the RSA algorithm can last up to 63204 ms (1 minute 22 seconds) while the Dual Modulus RSA algorithm lasts up to 248494123 ms (142 minutes 47 seconds).

Retrieval of ice cloud properties with a dual frequency optimal estimation algorithm for terahertz and millimeter wave cloud radar

Retrieval of ice cloud properties with a dual frequency optimal estimation algorithm for terahertz and millimeter wave cloud radar

Research on The Optimal Solution of Lagrangian Multiplier Function Method in Nonlinear Programming

For the general nonlinear constrained optimization model, this article will propose a new nonlinear Lagrange function, discuss the properties of the function at the KKT point, and prove that under appropriate conditions, the iterative point generated by the dual algorithm based on the function The column is locally convergent, and then an error estimate of the solution related to the penalty parameter is given. This provides a new way to solve nonlinear constrained optimization problems.

A dual simplex-type algorithm for the smallest enclosing ball of balls

We define the notion of infimum of a set of points with respect to the second order cone. This problem can be showed to be equivalent to the minimum ball containing a set of balls problem and to the maximum intersecting ball problem, as well as others. We present a dual algorithm which can be viewed as an extension of the simplex method to solve this problem.

Dual Variable Inertial Accelerated Algorithm for Split System of Null Point Equality Problems

In this paper, we introduce a novel dual variable algorithm accelerated via inertial extrapolation for solving the generalized split inverse problem given as a task of finding the common null point equality of finite family of inverse-strongly monotone mappings in Hilbert spaces. The proposed method uses the dual variable and self-adaptive technique, along with an inertial strategy which aims at getting accelerated convergence. We establish the convergence Theorem of the proposed method under some suitable assumptions. We also apply our result to solve several types of problems. Our results improve and generalize the corresponding several known results announced by many others. Numerical experiments are presented to show the efficiency and comparative performance of the proposed algorithm.

Fast Frequent Item Mining from Big Data using Map Reduce and Bit Vectors

One of the most important areas that are constantly being focused recently is the big data and mining frequent patterns from them is an interesting vertical which is perpetually being evolved and gained plethora of attention among the research fraternities. Generally, the data is mined with the aid of Apriori based algorithms, tree based algorithm and hash based algorithm but most of these existing algorithms suffer many snags and limitations. This paper proposes a new method that overrides and overcomes the most common problems related to speed, memory consumption and search space. The algorithm named Dual Mine employs binary vector representation and vertical data representations in the map reduce and then discover the most patterns from the large data sets. The Dual mine algorithm is then compared with some of the existing algorithms to determine the efficiency of the proposed algorithm and from the experimental results it is quite evident that the proposed algorithm “Dual Mine” outscored the other algorithms by a big magnitude with respect to speed and memory.

A Golden Ratio Primal–Dual Algorithm for Structured Convex Optimization

We design, analyze and test a golden ratio primal–dual algorithm (GRPDA) for solving structured convex optimization problem, where the objective function is the sum of two closed proper convex functions, one of which involves a composition with a linear transform. GRPDA preserves all the favorable features of the classical primal–dual algorithm (PDA), i.e., the primal and the dual variables are updated in a Gauss–Seidel manner, and the per iteration cost is dominated by the evaluation of the proximal point mappings of the two component functions and two matrix-vector multiplications. Compared with the classical PDA, which takes an extrapolation step, the novelty of GRPDA is that it is constructed based on a convex combination of essentially the whole iteration trajectory. We show that GRPDA converges within a broader range of parameters than the classical PDA, provided that the reciprocal of the convex combination parameter is bounded above by the golden ratio, which explains the name of the algorithm. An $$\mathcal {O}(1/N)$$ ergodic convergence rate result is also established based on the primal–dual gap function, where N denotes the number of iterations. When either the primal or the dual problem is strongly convex, an accelerated GRPDA is constructed to improve the ergodic convergence rate from $$\mathcal {O}(1/N)$$ to $$\mathcal {O}(1/N^2)$$ . Moreover, we show for regularized least-squares and linear equality constrained problems that the reciprocal of the convex combination parameter can be extended from the golden ratio to 2 and meanwhile a relaxation step can be taken. Our preliminary numerical results on LASSO, nonnegative least-squares and minimax matrix game problems, with comparisons to some state-of-the-art relative algorithms, demonstrate the efficiency of the proposed algorithms.

Analysis on dual algorithms for optimal cluster head selection in wireless sensor network

Clustering is the approach, which is utilized for aggregating the nodes as a group called clusters, which is used for reducing the routing overheads. This is a fundamental approach to extend the life expectancy of Wireless Sensor Network. However, the main challenge in WSN is the cluster head selection while taking the energy stabilization into account. Optimization within the WSN is the outstanding concern to provide intellect for the extensive period of network lifetime. Since clustering is a topological control method to decrease the process of SNs, it extensively improves overall system scalability and energy efficiency. Moreover, the appropriate selection of CH plays crucial role for attaining sustainable WSN. This paper proposes the firefly contribution with Firefly Cyclic Randomization (FCR) for the selection of cluster head in WSN. The randomly created solution in this algorithm is found based on three distribution functions like Uniform, Normal, and Gamma distributions. Moreover, the analysis is made on the second algorithm Firefly Cyclic Grey Wolf Optimization (FCGWO) by modifying $$r^{1}$$ and $$r^{2}$$ (random vectors) of Grey Wolf Optimization. In reality, the FCR and FGCGWO algorithms are planned on selecting the optimal cluster head by concentrating mainly on minimization of delay, minimization of the distance between nodes, and stabilization of energy. The analysis is performed and explained in terms of alive nodes, network lifetime, and energy efficiency under the three distributions.

A Novel Metagenomic Workflow for Biomonitoring across the Tree of Life using PCR-free Ultra-deep Sequencing of Extracellular eDNA

Biodiversity is declining on a planetary scale at an alarming rate due to anthropogenic factors. Classical biodiversity monitoring approaches are time-consuming, resource-intensive, and not scalable to address the current biodiversity crisis. The environmental DNA-based next-generation biomonitoring framework provides an efficient, scalable, and holistic solution for evaluating changes in various ecological entities. However, its scope is currently limited to monitoring targeted groups of organisms using metabarcoding, which suffers from various PCR-induced biases. To utilise the full potential of next-generation biomonitoring, we intended to develop PCR-free genomic technologies that can deliver unbiased biodiversity data across the tree of life in a single assay. Here, we present a novel metagenomic workflow comprising of a lysis-free extracellular DNA enrichment protocol from large-volume filtered water samples, a completely PCR-free library preparation step, an ultra-deep next-generation sequencing, and a pseudo-taxonomic assignment strategy using the dual lowest common ancestor algorithm. We demonstrate the utility of our approach in a pilot-scale spatially-replicated experimental setup in Chilika, a large hyper-diverse brackish lagoon ecosystem in India. Using incidence-based statistics, we show that biodiversity across the tree of life, from microorganisms to the relatively low-abundant macroorganisms such as Arthropods and Fishes, can be effectively detected with about one billion paired-end reads using our reproducible workflow. With decreasing costs of sequencing and the increasing availability of genomic resources from the earth biogenome project, our approach can be tested in different ecosystems and adapted for large-scale rapid assessment of biodiversity across the tree of life. *1

Local Convergence Analysis of a Primal–Dual Method for Bound-Constrained Optimization Without SOSC

We propose a local convergence analysis of a primal–dual interior point algorithm for the solution of a bound-constrained optimization problem. The algorithm includes a regularization technique to prevent singularity of the matrix of the linear system at each iteration, when the second-order sufficient conditions do not hold at the solution. These conditions are replaced by a milder assumption related to a local error-bound condition. This new condition is a generalization of the one used in unconstrained optimization. We show that by an appropriate updating strategy of the barrier parameter and of the regularization parameter, the proposed algorithm owns a superlinear rate of convergence. The analysis is made thanks to a boundedness property of the inverse of the Jacobian matrix arising in interior point algorithms. An illustrative example is given to show the behavior and the gain obtained by this regularization strategy.

Robust optimization of microgrid based on renewable distributed power generation and load demand uncertainty

The uncertainty of renewable distributed energy (photovoltaic, wind power, etc.) and load demand in the microgrid poses challenges to the economy and safety of microgrid operation. This paper proposes a robust optimization model of microgrid considering uncertainty to take into account the economy and robustness of microgrid operation. A two-stage robust optimization model is established to find a balance between the economy and robustness of microgrid operation. Through the optimization procedure, the robust adjustment parameters for microgrid operation can be obtained. The optimized can effectively balance the economy and robustness. The Benders dual algorithm is used to solve the established two-stage robust optimization model. The CPLEX solver is used to simulate the IEEE39-bus system to verify the feasibility and effectiveness of the method. The simulation results show that the robustness of the system can be achieved by solving the robust adjustment parameters, meanwhile the operating cost can be reduced as much as possible no matter in the buying electricity scenario or in the selling electricity scenario.

A primal–dual algorithm for risk minimization

In this paper, we develop an algorithm to efficiently solve risk-averse optimization problems posed in reflexive Banach space. Such problems often arise in many practical applications as, e.g., optimization problems constrained by partial differential equations with uncertain inputs. Unfortunately, for many popular risk models including the coherent risk measures, the resulting risk-averse objective function is nonsmooth. This lack of differentiability complicates the numerical approximation of the objective function as well as the numerical solution of the optimization problem. To address these challenges, we propose a primal–dual algorithm for solving large-scale nonsmooth risk-averse optimization problems. This algorithm is motivated by the classical method of multipliers and by epigraphical regularization of risk measures. As a result, the algorithm solves a sequence of smooth optimization problems using derivative-based methods. We prove convergence of the algorithm even when the subproblems are solved inexactly and conclude with numerical examples demonstrating the efficiency of our method.

Deformable Image Registration Based on Functions of Bounded Generalized Deformation

Functions of bounded deformation (BD) are widely used in the theory of elastoplasticity to describe the possibly discontinuous displacement fields inside elastoplastic bodies. BD functions have been proved suitable for deformable image registration, the goal of which is to find the displacement field between a moving image and a fixed image. Recently BD functions have been generalized to symmetric tensor fields of bounded generalized variation. In this paper, we focus on the first-order symmetric tensor fields, i.e., vector-valued functions, of bounded generalized variation. We specify these functions as functions of bounded generalized deformation (BGD) since BGD functions are natural generalizations of BD functions. We propose a BGD model for deformable image registration problems by regarding concerned displacement fields as BGD functions. BGD model employs not only the first-order but also higher-order coupling information of components of the displacement field. It turns out that BGD model allows for jump discontinuities of displacements while, in contrast to BD model, at the same time is able to employ higher-order derivatives of displacements in smooth regions. As a result, BGD model tends to capture possible discontinuities of displacements appeared around edges of the target objects while keep the smoothness of displacements inside the target objects as well. This characteristic enables BGD model to obtain better registration results than BD model and other variational models. To our knowledge, it is the first time in literature to use BGD functions for image registration. A first-order adaptive primal–dual algorithm is adopted to solve the proposed BGD model. Numerical experiments on 2D and 3D images show both effectiveness and advantages of BGD model.