Finite Number Of Iterations Research Articles

Synergetic information bottleneck for joint multi-view and ensemble clustering

Multi-view and ensemble clustering methods have been receiving considerable attention in exploiting multiple features of data. However, both of these methods have their own set of limitations. Specifically, the performance of multi-view clustering may degrade due to the conflict between heterogeneous features, while ensemble clustering relies heavily on the quality of basic clusterings since it discovers the final clustering partition without considering the original feature structures of the source data. In this study, we propose a novel clustering scheme called synergetic information bottleneck (SIB) for joint multi-view and ensemble clustering. First, the proposed SIB utilizes multiple original features to characterize data information from different views while exploiting the basic clusterings to relieve the conflict of heterogeneous features. Second, the SIB generally formulates the problem of joint multi-view and ensemble clustering as a function of mutual information maximization, in which the relatedness between the original features and auxiliary basic clusterings is maximally preserved with respect to the final clustering partition. Finally, to optimize the objective function of SIB, a novel “draw-and-merge” optimization method is proposed. In addition, we prove that this novel optimization method can ensure that the objective function of SIB converges to a stable optimal in a finite number of iterations. Extensive experiments conducted on several practical tasks demonstrate that the SIB outperforms the state-of-the-art multi-view and ensemble clustering methods.

Partially doubly symmetric solutions of general Sylvester matrix equations

The study of linear matrix equations is extremely important in many scientific fields such as control systems and stability analysis. In this work, we aim to design the Hestenes-Stiefel (HS) version of biconjugate residual (Bi-CR) algorithm for computing the (least Frobenius norm) partially doubly symmetric solution [Formula: see text] of the general Sylvester matrix equations [Formula: see text] for [Formula: see text]. We show that the proposed algorithm converges in a finite number of iterations. Finally, numerical results compare the proposed algorithm to alternative algorithms.

Performance Research on Iterative Methods for Image Deblurring

This paper introduces the iterative image restoration algorithms for the elimination of linearly varying blurs from the images degraded by motion blur and additive noise. Iterative algorithms are very operative for this applications since they include different types of prior knowledge about the class of reasonable solutions. These algorithms are robust in nature to the errors in estimating the blurring operators and can be used to remove the non-stationary blurs. Performance analysis and limitations of traditional approaches such as Inverse, Wiener and Constrained Least Square filters (CLS) are discussed with respect to the iterations. Role and choice of imposing a constraint on the solutions of the algorithms which gives better restoration results are discussed. Regularization methods are debated to Minimis extreme noise amplifications due to ill-posed conditions in the inverse deblurring problems and it is shown that the reduction of noise effects can be achieved by terminating the algorithm after finite number of iterations. It is shown that restoration algorithms with constraints and spatially adaptability reduces the effects of ringing artifacts significantly. The rate of convergence of the algorithms based on the variations in the number of iterations are discussed and performance analysis, limitations and Comparison with the experimental results are presented.

Design of a free-form diffuser for the entrance optic to correct the cosine error in the photometer.

The entrance optic is an important part of the photometer head. It can match the directional response of the photometer to the cosine function. In this paper, an entrance optic consisting of a free-form diffuser, a shadow ring, and an integrating cavity is introduced. An iterative optimization algorithm is presented to design a free-form diffuser that exhibits better cosine response characteristics. Diffusers of different materials and sizes are designed in a simulation experiment. After a finite number of iterations, in the absence of the shadow ring, the integral cosine error of the free-form diffuser is less than 1%. The directional cosine error is less than 3% for incidence angles between 0° and 70°. After adding a shadow ring to correct the directional response of the incident angle greater than 80°, for incident angles between 0° and 85°, the cosine errors are typically less than 3%, except that the cosine errors of very few large incident angles are close to 5%. The experimental results show the effectiveness and robustness of the proposed method. In addition, the influence of an important percentage constant σ on iterative optimization is studied. It is found that the larger the parameter σ, the fewer the number of iterations, and the directional cosine error may be slightly larger but still acceptable. The wide range of values of σ further embodies the versatility and flexibility of the proposed method.

Distributed Management Systems for Infocommunication Networks: A Model Based on TM Forum Frameworx

The existing management systems for networks and communication services do not fully meet the demands of users in next-generation infocommunication services that are dictated by the business processes of companies. Open digital architecture (ODA) is able to dramatically simplify and automate main business processes using the logic of distributed computing and management, which allows implementing services on a set of network nodes. The performance of a distributed operational management system depends on the quality of solving several tasks as follows: the distribution of program components among processor modules; the prioritization of business processes with parallel execution; the elimination of dead states and interlocks during execution; and the reduction of system cost to integrate separate components of business processes. The program components can be distributed among processor modules by an iterative algorithm that calculates the frequency of resource conflicts; this algorithm yields a rational distribution in a finite number of iterations. The interlocks of parallel business processes can be eliminated using the classic file sharing example with two processes and also the methodology of colored Petri nets. The system cost of integration processes in a distributed management system is reduced through partitioning the network into segments with several controllers that interact with each other and manage the network in a coordinated way. This paper develops a model of a distributed operational management system for next-generation infocommunication networks that assesses the efficiency of operational activities for a communication company.

Decentralized path planning for cooperating autonomous mobile units

In various domains, e.g. robotics or autonomous driving, automated path planning for conflict-free movements of the participating vehicles, i.e. robots, cars or other mobile units is an essential task on the navigation level. Especially in crowded scenarios in which many vehicles share a common operation area together with other static or dynamic obstacles, finding a set of conflict-free paths for all vehicles is a challenging navigation task that is crucial for fully autonomous vehicles. In this work we propose a decentralized path planning algorithm for such scenarios which focuses on the cooperative negotiation of conflict-free paths. The path planning on navigation level is realized with an innovative graph search algorithm based on A* that incorporates dynamic obstacles (e.g. manually operated vehicles and other autonomous mobile units) and enables the autonomous vehicles to change speed. Furthermore, the framework suggests a decentralized approach, in which each vehicle performs its own path planning locally. Communication between the mobile units allows them to cooperatively negotiate conflict-free paths for all autonomous vehicles participating in the framework. The resulting iterative process of calculating new paths and negotiating a feasible solution set for all vehicles is designed to yield a deterministic solution within a finite number of iterations. We furthermore provide promising simulation results for this framework with test scenarios involving many autonomous vehicles and challenging obstacle formations.

An efficient and social-aware distributed in-network caching scheme in named data networks using matching theory

One of the main characteristics of Named Data Networks (NDN) which makes it a promising architecture for the future of the Internet is its universal in-network caching. Due to the limited caching capacity of the network and the infinite amount of data objects, the cache management scheme becomes a challenging task in NDN. While existing cache management schemes utilize network’s caching capacity inefficiently by redundantly keeping popular objects across the network and concentrate on improving bandwidth utilization, we focus on a novel criterion to elevate the cache utilization efficiency. In this paper, a distributed solution that associates the objects to the cache-enabled nodes and maximizes the total network’s social welfare is proposed which models the problem of network’s social welfare maximization as a many-to-one matching game. Further, it is proved that the proposed solution has a number of desired properties. The resulting matching is stable and the outcome of the proposed algorithm is in Competitive Equilibrium, the social-welfare of the proposed algorithm converges to the social-welfare of the centralized optimal approach as the price step number is sufficiently small, the proposed algorithm converges after a finite number of iterations with relatively low overhead and the cost of retrieving the required objects is the minimum for the Internet Service Providers (ISP). Finally, simulation results show the convergence of our proposed scheme to the centralized optimal solution and its outperformance against the default applied caching scheme in NDN in terms of both network’s social welfare and hit ratio.

Improved time-censored reliability test plans for k-out-of-n gamma systems

Relevant prior knowledge supported by historical data and expert judgments is common in many manufacturing processes. The classical viewpoint to the determination of acceptance sampling plans for k-out-of-n gamma systems is generalized to those situations in which the available previous information is appreciable. A beta distribution with a reduced parameter space is adopted to describe the stochastic behavior of the fraction of defective systems. An integer nonlinear programming problem is stated to find the inspection scheme that minimizes the required number of components to test and keeps the average producer and consumer risks below specified thresholds. First, lower and upper bounds, as well as an approximate solution, are derived. Then, an efficient step-by-step procedure, which finds the best acceptance sampling plan in a finite number of iterations, is provided. The inclusion of prior information into the decision process provides substantial savings in the sample size required for demonstrating system reliability, and also more accurate assessments of the actual producer and consumer risks. A system of five water pumps for cooling a reactor is analyzed for illustrative and comparative purposes.

Properties of approximated empirical mode decomposition and optimal design of its system kernel matrix for signal decomposition

An approximated empirical mode decomposition generates a set of approximated intrinsic mode functions via a linear, nonadaptive but iterative approach. The decomposition was found to be very useful for a content-independent pattern recognition application. As the process is characterized by a system kernel matrix and performed iteratively, the approximated intrinsic mode functions can be understood as the original signals processed by a set of mask operations. Here, some properties of the decomposition are studied and an optimal design of the system kernel matrix is proposed. It is found that there is only one approximated intrinsic mode function if the exact perfect reconstruction condition is satisfied. Obviously, the approximated intrinsic mode function is the original signal. Therefore, the decomposition is practically not meaningful. To address this issue, the infinite number of iterations in the algorithm is truncated to a finite number of iterations. Also, the design of the system kernel matrix is formulated as an optimization problem. In particular, the exact perfect reconstruction error between the sum of the approximated intrinsic mode functions and the original signal is minimized and the total absolute sum of the difference between any two different eigenvalues of the iterative matrix is maximized subject to a stability condition. Here, the stability condition refers to the eigenvalues of the iterative matrix being between zero and one. Since the optimization problem is nonsmooth and nonconvex, a genetic algorithm is employed for finding its near global optimal solution. Compared to the conventional approximated empirical mode decomposition, computer numerical simulations show that our proposed approach can achieve more than one approximated intrinsic mode function with each approximated intrinsic mode function corresponding to an output of a more meaningful mask operation.

BEAUTY IN MATHEMATICAL EDUCATION: SYNERGETIC WORLDVIEW

Introduction. The most important concepts underlying beauty are the mathematical concepts of symmetry and fractality. These categories are fundamental for modern mathematics, science and culture in general. However, in mathematical education and pedagogical literature, the ratio of these main categories has not been considered yet. Of special interest is the fact that the concepts of fractals, fractality and fractal geometry and fractal graphics are not included in the vast majority of high school programmes, although they have become commonly used among mathematicians and graphic designers.The aims of the article were the following: to demonstrate intersectionality and correlations of the basic concepts of symmetry and fractals from the point of view of synergetics, to establish the relevance of studying these concepts in the course of mathematics for aesthetic education of students and development of their worldview.Methodology and research methods. A significant role in the study is given to post-non-classical methodology based on synergetic worldview. The author employed the provisions of trinitarian methodology: in addition to two binary oppositions, the third element is necessary to solve the problem of contradiction of theseoppositions and integration into one coherent whole as the onditions of their coexistence. In the course of the research, analysis and generalisation of pedagogical and methodical literature, methods of comparative, historical and logical types of analysis were used.Results and scientific novelty.For centuries, beauty has been understood as a stable order and symmetry. The synergetrics as a general scientific theory about self-organisation of complex systems allows us to give another interpretation of beauty – as a kind of attractor, the result of self-organisation of nature or theflight of human thought. In the most general view, symmetry can be considered as transformation of similarity, which is also the core of another concept – fractality. On the one hand, fractality can be considered as one of the manifestations of symmetry in the broad sense. On the other hand, symmetry can be considered as a manifestation of fractality with a finite number of iterations. Thus, the concepts of symmetry and fractality are closely interrelated. Symmetry and fractality are two opposites, mutually complementing each other, aesthetically and mathematically mutually passing into each other. Symmetry reveals the beauty of a sustainable order and fractality reflects the beauty of the result of self-organisation of the chaos of nature or the freedom of the human mind. Therefore, symmetry and fractals are the most important concepts for the disclosure of the beauty of the universe, which determines their importance for mathematical learning and for aesthetic education of students.Practical significance. Taking into account the fact that the concepts of symmetry and fractals are directly related to each other, they should be jointly-taught. This will contribute to the development concept of mathematics education: to increase motivation for mathematical studies, to develop cognitive interests and activities, to narrow the gap between education and research processes, to overcome the problems with aesthetic education of students.

A Branch-and-Cut Benders Decomposition Algorithm for Transmission Expansion Planning

The emergence of a great number of regional planning projects worldwide has considerably increased the complexity and relevance of transmission expansion planning, prompting intensive research and investigation on the formulation and solution. In this paper, the security constrained transmission expansion planning problem is addressed by a branch-and-cut Benders decomposition (BCBD) algorithm. It is a deterministic method where the global optimal solution can be guaranteed in a finite number of iterations. Based on this implementation framework, four acceleration strategies have been employed to enhance the performance. For the validation of accuracy and efficiency, the commercial solver Cplex running on the same platform is introduced for comparison, where four types of mixed-integer linear programming algorithms are discriminated by specifying two pairs of key settings, including dynamic searching and parallel implementation. The superiority of BCBD over Cplex has been validated by case studies, where five benchmark systems ranging from 6 to 300 buses are employed. In addition, performance analysis between BCBD and classical Benders decomposition has also been carried out to distinguish the contribution of branch-and-cut framework and acceleration strategies.

Revisiting Approximate Linear Programming: Constraint-Violation Learning with Applications to Inventory Control and Energy Storage

Approximate linear programs (ALPs) are well-known models for computing value function approximations (VFAs) of intractable Markov decision processes (MDPs). VFAs from ALPs have desirable theoretical properties, define an operating policy, and provide a lower bound on the optimal policy cost. However, solving ALPs near-optimally remains challenging, for example, when approximating MDPs with nonlinear cost functions and transition dynamics or when rich basis functions are required to obtain a good VFA. We address this tension between theory and solvability by proposing a convex saddle-point reformulation of an ALP that includes as primal and dual variables, respectively, a vector of basis function weights and a constraint violation density function over the state-action space. To solve this reformulation, we develop a proximal stochastic mirror descent (PSMD) method that learns regions of high ALP constraint violation via its dual update. We establish that PSMD returns a near-optimal ALP solution and a lower bound on the optimal policy cost in a finite number of iterations with high probability. We numerically compare PSMD with several benchmarks on inventory control and energy storage applications. We find that the PSMD lower bound is tighter than a perfect information bound. In contrast, the constraint-sampling approach to solve ALPs may not provide a lower bound, and applying row generation to tackle ALPs is not computationally viable. PSMD policies outperform problem-specific heuristics and are comparable or better than the policies obtained using constraint sampling. Overall, our ALP reformulation and solution approach broadens the applicability of approximate linear programming.This paper was accepted by Yinyu Ye, optimization.

Optimal network-level traffic signal control: A benders decomposition-based solution algorithm

This paper formulates the network-level traffic signal timing optimization problem as a Mixed-Integer Non-Linear Program (MINLP) and presents a customized methodology to solve it with a tight optimality gap. The MINLP is based on the Cell Transmission Model (CTM) network loading concept and captures the fundamental flow-density diagram of the CTM explicitly by considering closed-form constraints in the model and thus, eliminates the flow holding-back problem. The proposed solution algorithm is based on the Benders decomposition technique and decomposes the original MINLP to an equivalent Integer Program (IP) (Master problem), and a new MINLP (Primal problem). We will show that the new MINLP has only one optimal non-holding-back solution that can be found by a CTM simulation run. We will prove that the proposed solution technique guarantees convergence to optimal solutions with a finite number of iterations. Furthermore, we propose a dual estimation algorithm for the new MINLP (the Primal problem), which utilizes a simulation-based approach to generate Benders cuts instead of solving a complex optimization program. We applied the proposed solution technique to a simulated network of 20 intersections under various demand patterns and observed an optimality gap of at most 2% under all tested conditions. We compared the solutions of the proposed algorithm with two benchmark algorithms and found reductions in total travel time ranging from 7.0% to 35.7%.

On the Deepest Fallacy in the History of Mathematics: The Denial of the Postulate about the Approximation Nature of a Simple-Iteration Method and Iterative Derivation of Cramer’s Formulas

Contrary to the opinion about approximation nature of a simple-iteration method, the exact solution of a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix is demonstrated. We present a theorem and its proof that confirms the possibility to obtain the finite process and imposes the requirement for the matrix of SLAE. This matrix must be unipotent, i.e. all its eigenvalues to be equal to 1. An example of transformation of SLAE given analytically to the form with a unipotent matrix is presented. It is shown that splitting the unipotent matrix into identity and nilpotent ones results in Cramer’s analytical formulas in a finite number of iterations.

A Simple Iterative Method for Exact Solution of Systems of Linear Algebraic Equations

We present for the first time a theorem (with proof) of solving a system of linear algebraic equations (SLAE) in a finite number of iterations with a stationary matrix. The system is transformed such that the spectrum of the matrix to be unit. Splitting the matrix gives a nilpotent matrix of the iteration system that generates an exact solution of SLAE for a number of iterations not exceeding the dimension of the system.

КОНЕЧНОЕ ЧИСЛО ИТЕРАЦИЙ В ДВУХЭТАПНЫХ АЛГОРИТМАХ ДЛЯ РЕШЕНИЯ ЗАДАЧ О РАВНОВЕСИИ

A two iterative two-stage proximal algorithms for the approximate solution of the equilibrium problem in a Hilbert space is considered. In this article we proved the convergence of algorithms in a finite number of iterations when the condition of sharpness is fulfilled.

Using regularization and second order information in outer approximation for convex MINLP

In this paper, we present two new methods for solving convex mixed-integer nonlinear programming problems based on the outer approximation method. The first method is inspired by the level method and uses a regularization technique to reduce the step size when choosing new integer combinations. The second method combines ideas from both the level method and the sequential quadratic programming technique and uses a second order approximation of the Lagrangean when choosing the new integer combinations. The main idea behind the methods is to choose the integer combination more carefully at each iteration, in order to obtain the optimal solution in fewer iterations compared to the original outer approximation method. We prove rigorously that both methods will find and verify the optimal solution in a finite number of iterations. Furthermore, we present a numerical comparison of the methods based on 109 test problems to illustrate their advantages.

BCR Algorithm for Solving Quadratic Inverse Eigenvalue Problems for Partially Bisymmetric Matrices

AbstractThe inverse eigenvalue problem appears repeatedly in a variety of applications. The aim of this paper is to study a quadratic inverse eigenvalue problem of the form AXΛ2 + BXΛ + CX = 0 where A, B and C should be partially bisymmetric under a prescribed submatrix constraint. We derive an efficient matrix method based on the Hestenes‐Stiefel (HS) version of biconjugate residual (BCR) algorithm for solving this constrained quadratic inverse eigenvalue problem. The theoretical results demonstrate that the matrix method solves the constrained quadratic inverse eigenvalue problem within a finite number of iterations in the absence of round‐off errors. Finally we validate the accuracy and efficiency of the matrix method through the numerical results.

Modified mean shift algorithm

The mean shift (MS) algorithm is an iterative method introduced for locating modes of a probability density function. Although the MS algorithm has been widely used in many applications, the convergence of the algorithm has not yet been proven. In this study, the authors modify the MS algorithm in order to guarantee its convergence. The authors prove that the generated sequence using the proposed modified algorithm is a convergent sequence and the density estimate values along the generated sequence are monotonically increasing and convergent. In contrast to the MS algorithm, the proposed modified version does not require setting a stopping criterion a priori; instead, it guarantees the convergence after a finite number of iterations. The proposed modified version defines an upper bound for the number of iterations which is missing in the MS algorithm. The authors also present the matrix form of the proposed algorithm and show that, in contrast to the MS algorithm, the weight matrix is required to be computed once in the first iteration. The performance of the proposed modified version is compared with the MS algorithm and it was shown through the simulations that the proposed version can be used successfully to estimate cluster centres.

A novel use of value iteration for deriving bounds for threshold and switching curve optimal policies

AbstractIn this article, we develop a novel role for the initial function v0 in the value iteration algorithm. In case the optimal policy of a countable state Markovian queueing control problem has a threshold or switching curve structure, we conjecture, that one can tune the choice of v0 to generate monotonic sequences of n‐stage threshold or switching curve optimal policies. We will show this for three queueing control models, the M/M/1 queue with admission and with service control, and the two‐competing queues model with quadratic holding cost. As a consequence, we obtain increasingly tighter upper and lower bounds. After a finite number of iterations, either the optimal threshold, or the optimal switching curve values in a finite number of states is available. This procedure can be used to increase numerical efficiency.