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American Control Conference

作者： Mukaidani, H Hiroshima Univ Grad Sch Educ Higashihiroshima 7398524 Japan

ISBN: (纸本)0780383354

In this paper, the linear quadratic N-players Nash games for infinite horizon large-scale systems are discussed. Nash strategies are obtained by solving the cross-coupled algebraic Riccati equations (CARE) via the numerical technique. The asymptotic expansions for the CARE are newly established. The main contribution in this paper is that the linear convergence of the proposed algorithm which is based on the fixed point algorithm is proved. In order to demonstrate the efficiency of the algorithm, numerical example is given for the practical power systems.

关键词： large-scale systems linear quadratic control infinite horizon game theory Riccati equations convergence of numerical methods numerical computation linear quadratic N-players Nash games infinite horizon large scale systems cross coupled algebraic Riccati equations numerical technique linear convergence fixed point algorithm large-scale systems numerical calculation Riccati equations convergence of numerical methods infinite horizon linear quadratic control Numerical methods fixed point

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Adaptive Dictionary-Based Spatio-temporal Flow Estimation for Echo PIV 10

Adaptive Dictionary-Based Spatio-temporal Flow Estimation fo...

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10th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR)

作者： Bodnariuc, Ecaterina Gurung, Arati Petra, Stefania Schnoerr, Christoph Heidelberg Univ Image & Pattern Anal Grp D-69115 Heidelberg Germany Delft Univ Technol Lab Aero & Hydrodynam P&E 3ME NL-2600 AA Delft Netherlands

ISBN: (纸本)9783319146126;9783319146119

We present a novel approach to detect the trajectories of particles by combining (a) adaptive dictionaries that model physically consistent spatio-temporal events, and (b) convex programming for sparse matching and trajectory detection in image sequence data. The mutual parametrization of these two components are mathematically designed so as to achieve provable convergence of the overall scheme to a fixed point. While this work is motivated by the task of estimating instantaneous vessel blood flow velocity using ultrasound image velocimetry, our contribution from the optimization point of view may be of interest also to related pattern and image analysis tasks in different application fields.

关键词： motion estimation fixed point algorithm adaptive dictionaries sparse representation sparse error correction Echo PIV

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algorithms with high order convergence speed for blind source extraction

Algorithms with high order convergence speed for blind sourc...

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Conference on High Performance algorithms and Software for Nonlinear Optimization

作者： Georgiev, Pando Pardalos, Panos Cichocki, Andrzej Univ Cincinnati ECECS Dept Cincinnati OH 45221 USA Sofia Univ St K1 Ohridski Sofia 1164 Bulgaria Univ Florida Ctr Appl Optimizat Gainesville FL 32611 USA RIKEN Brain Sci Inst Wako Saitama 3510198 Japan

A rigorous convergence analysis for the fixed point ICA algorithm of Hyvarinen and Oja is provided and a generalization of it involving cumulants of an arbitrary order is presented. We consider a specific optimization problem OP(p), p > 3, integer, arising from a Blind Source Extraction problem (BSE) and prove that every local maximum of OP(p) is a solution of (BSE) in sense that it extracts one source signal from a linear mixture of unknown statistically independent signals. An algorithm for solving OP(p) is constructed, which has a rate of convergence p - 1.

关键词： independent component analysis cumulants fixed point algorithm

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Dynamic Supply Chain Model and Disruption Analysis

Dynamic Supply Chain Model and Disruption Analysis

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作者： Lee, Ilsoo PennState University Libraries

学位级别：Doctor of Philosophy

Rapid changes and complexities in business environments have stressed the interactions between partners and competitors, leading supply chains to become the most important element of contemporary business environments. This dissertation shows how to structuralize complex supply chain to create integrated dynamic models of supply chains using differential variational inequalities under the assumption that the output market for the firms is organized as a non-cooperative spatial oligopoly. Production planning and distribution plans for finished goods are determined by dynamic oligopolistic competition among their producers. In addition to these assumptions, integrated supply chain model assumes that input factor prices are set by contracts extending over the planning horizon and that just-in-time use of factor inputs is pervasive. Furthermore, with the potential of causing financial, reputational, and operational loss, supply chain disruption must be managed through the optimized planning and design of supply chain networks. Finally, this dissertation presents a mathematically dynamic supply chain network model threatened by disruptions and formulates a mathematical model as differential variational inequalities(DVI). The DVI is solved using a fixed-point algorithm, and finally a simple numerical example, introduced to compare supply chain optimization with and without disruptions, is presented.

关键词： Non-cooperative games Disruptions Dynamic supply chain network Differential variational inequalities fixed point algorithm

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Steady state population balance modelling of precipitation processes: Nucleation, growth and size-dependent agglomeration

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JOURNAL OF CRYSTAL GROWTH 2023年第1期616卷

作者： Vasquez, Cristian Camilo Ruiz Lebaz, Noureddine Ramiere, Isabelle Lalleman, Sophie Mangin, Denis Bertrand, Murielle Univ Montpellier CEA DES ISECDENDMRC Marcoule France Univ Claude Bernard Lyon 1 Univ Lyon CNRS LAGEPP UMR 5007 43 Blvd 11 novembre 1918 F-69100 Villeurbanne France CEA DES IRESNE DECSESC F-13108 St Paul Les Durance France

In this work a numerical methodology to solve the steady state Population Balance Equation (PBE) is developed. Three crystallisation mechanisms are included, namely: nucleation, size-independent growth and size-dependent loose agglomeration. The numerical method is based on the discretisation of the crystal size as distributed variable. In order to describe the loose agglomeration, the numerical methodology solves two PBE: one including the nucleation and growth mechanisms and one accounting for the agglomeration process. From the first PBE, liquid phase composition, supersaturation, developed crystal surface and Crystallite Size Distribution (CSD) are obtained. Similarly, the second PBE leads to the Agglomerate Size Distribution (ASD). The study of the size -dependant agglomeration kernel induces an additional numerical difficulty due to the dependency of both PBE and agglomeration kernel on the particle size. An accelerated fixed point algorithm based on the crossed secant method is adapted to overcome the difficulty and accurately solve the agglomeration PBE. The oxalic precipitation of uranium is simulated using this numerical methodology. First, the experimental results of a reference case are compared with the numerical predictions in terms of particle size distribution, mean size, mass fraction and moments. Then, the operating conditions are varied in order to test the algorithm robustness and performances. In all cases, the crossed secant method ensures the size-dependent agglomeration PBE solution and properly predicts the ASD. The developed numerical methodology predicts the mean particle size under the experimental uncertainty in a reasonable computation time and number of iterations.

关键词： A1 Population balance A2 Steady state Size-dependent agglomeration Oxalic precipitation fixed point algorithm Convergence acceleration

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A PDE-regularized smoothing method for space-time data over manifolds with application to medical data

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2022年第12期38卷 e3650-e3650页

作者： Ponti, Luca Perotto, Simona Sangalli, Laura M. Politecn Milan Milan Italy Politecn Milan MOX Dept Math Piazza Leonardo da Vinci 32 I-20133 Milan Italy

We propose an innovative statistical-numerical method to model spatio-temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regularizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in practical contexts, by dealing with neuroimaging and hemodynamic data.

关键词： finite elements fixed point algorithm hemodynamics neuroimaging regularized regression

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Near-Optimal Control for Singularly Perturbed Stochastic Systems

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2009年第11期E92A卷 2874-2882页

作者： Sagara, Muneomi Mukaidani, Hiroaki Yamamoto, Toru Prefectural Univ Kumamoto Fac Adm Kumamoto 8628502 Japan Hiroshima Univ Grad Sch Educ Higashihiroshima 7398524 Japan

This paper addresses linear quadratic control with state-dependent noise for singularly perturbed stochastic systems (SPSS). First, the asymptotic structure of the stochastic algebraic Riccati equation (SARE) is established for two cases. Second, a new iterative algorithm that combines Newton's method with the fixed point algorithm is established. As a result, the quadratic convergence and the reduced-order computation in the same dimension of the subsystem are attained. As another important feature, a high-order state feedback controller that uses the obtained iterative solution is given and the degradation of the cost performance is investigated for the stochastic case for the first time. Furthermore, the parameter independent controller is also given in case the singular perturbation is unknown. Finally, in order to demonstrate the efficiency of the proposed algorithm, a numerical example is given for the practical megawatt-frequency control problem.

关键词： stochastic LQ problem state-dependent noise Newton's method fixed point algorithm

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A general optimality criteria algorithm for a class of engineering optimization problems

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ENGINEERING OPTIMIZATION 2015年第5期47卷 674-688页

作者： Belegundu, Ashok D. Penn State Univ Dept Mech & Nucl Engn University Pk PA 16802 USA

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables.

关键词： optimality criteria re-sizing surrogate multiplier method nonlinear programming fixed point algorithm

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Numerical Computation for H ∞ State Feedback Control of Large-Scale Systems

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IFAC Proceedings Volumes 2004年第11期37卷 295-301页

作者： Hiroaki Mukaidani Graduate School of Education Hiroshima University. 1–1–1 Kagamiyama. Higashi-Hiroshima 739-8524 JAPAN.

In this paper, H ∞ state feedback control for large-scale systems is investigated. The attention is focused on the design of the high-order approximate H ∞ controller which is based on the numerical solutions. The novel contribution is that a new iterative algorithm is derived by combining the Kleinman algorithm and the fixed point algorithm. As a result, H ∞ controller can be constructed in the same dimension of the subsystems. It is newly proved that the proposed algorithm has the quadratic convergence. Moreover, it is shown that the resulting controller achieves O(E 2 k ) approximation of the optimal H ∞ cost.

关键词： Large-scale systems H ∞ state feedback control Kleinman algorithm fixed point algorithm

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Complete dictionary learning via l4-norm maximization over the orthogonal group

The Journal of Machine Learning Research

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The Journal of Machine Learning Research 2020年第1期21卷 6622-6689页

作者： Yuexiang Zhai Zitong Yang Zhenyu Liao John Wright Yi Ma Department of Electrical Engineering and Computer Science University of California Berkeley CA Kuaishou Technology Department of Electrical Engineering Columbia University New York NY

This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity. The recent l1-minimization based methods do provide such guarantees but the associated algorithms recover the dictionary one column at a time. In this work, we propose a new formulation that maximizes the l4-norm over the orthogonal group, to learn the entire dictionary. We prove that under a random data model, with nearly minimum sample complexity, the global optima of the l4-norm are very close to signed permutations of the ground truth. Inspired by this observation, we give a conceptually simple and yet effective algorithm based on "matching, stretching, and projection" (MSP). The algorithm provably converges locally and cost per iteration is merely an SVD. In addition to strong theoretical guarantees, experiments show that the new algorithm is significantly more efficient and effective than existing methods, including KSVD and l1-based methods. Preliminary experimental results on mixed real imagery data clearly demonstrate advantages of so learned dictionary over classic PCA bases.

关键词： sparse dictionary learning l4-norm maximization orthogonal group measure concentration fixed point algorithm

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