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Linear complementarity, linear and nonlinear programming
01 Jan 1988-
About: The article was published on 1988-01-01 and is currently open access. It has received 1012 citations till now. The article focuses on the topics: Mixed complementarity problem & Complementarity theory.
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01 Jan 2008
TL;DR: In this paper, a theoretisches Fundament for derartige mobile robotersysteme optimal einzusetzen is presented, based on the Theorie der Mehrkorperdynamik and der nichtglatten Mechanik.
Abstract: Ein auf einer mobilen Basis montierter Roboterarm ist in seinen kinetischen Moglichkeiten einem fest installierten Arm stets unterlegen: Eine zu hohe Traglast oder zu hohe Bewegungsdynamik kann ein Umkippen oder Weggleiten verursachen. Die Arbeit stellt, basierend auf der Theorie der Mehrkorperdynamik und der nichtglatten Mechanik, ein theoretisches Fundament bereit, um derartige mobile Robotersysteme optimal einzusetzen. Besondere Aufmerksamkeit kommt der Modellierung der Kontaktmechanik zwischen der Roboterbasis und der Umgebung als lineares Komplementaritatsproblem LCP in einer kompakten Formulierung unter Verwendung finiter Zustandsautomaten zur Beschreibung der Kontaktzustande zu. Es werden gewohnliche einseitige Bindungen und lokale Verspannungen berucksichtigt. Die vorgestellte Methodik wird bei statischen und dynamischen Optimierungsaufgaben angewandt und in experimentell umgesetzten Bahnplanungsszenarien erfolgreich validiert.
9 citations
Cites background from "Linear complementarity, linear and ..."
...CISM Courses and Lectures, Montpellier, Springer-Verlag, 1987 [109] MURTY, K....
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...Im Hinblick auf die Linearität des Problems wurden zur Lösung von LCPs eine Vielzahl unterschiedlicher Pivotalgorithmen entwickelt [35] [109]....
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...in [34] [35] [65] und [109] detailliert dargestellt und sollen hier nicht weiter vertieft werden....
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TL;DR: This approach can be employed to minimize any strictly convex quadratic function over a polyhedral set and is shown to be more effective than other existing methods for solving these problems.
Abstract: In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that this approach can be employed to minimize any strictly convex quadratic function over a polyhedral set. Through a computational experiment we evaluate the effectiveness of this approach and show that for a collection of randomly generated instances this approach is more effective than other existing methods for solving these problems.
9 citations
TL;DR: In this article, a modulus-based Levenberg-Marquardt method with non-monotone line search is presented and the global convergence result is obtained.
Abstract: As applying the Levenberg-Marquardt method to the reformulation of linear complementarity problem, a modulus-based Levenberg-Marquardt method with nonmonotone line search is established and the global convergence result is presented. Numerical experiments show that the proposed method is efficient and outperforms the modulus-based matrix splitting iteration method. AMS subject classifications: 90C33, 65F10
9 citations
Cites background from "Linear complementarity, linear and ..."
..., the linear and quadratic programming, the economies with institutional restrictions upon prices, the optimal stopping in Markov chain, and the free boundary problems; see [2,3,5] for details....
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TL;DR: In this article, a cone complementary problems (CCPCCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately.
Abstract: Nonsmooth dynamics algorithms have been widely used to solve the problems of frictional contact dynamics of multibody systems. The linear complementary problems (LCP) based algorithms have been proved to be very effective for the planar problems of frictional contact dynamics. For the spatial problems of frictional contact dynamics, however, the nonlinear complementary problems (NCP) based algorithms usually achieve more accurate results even though the LCP based algorithms can evaluate the friction force and the relative tangential velocity approximately. In this paper, a new computation methodology is proposed to simulate the nonsmooth spatial frictional contact dynamics of multibody systems. Without approximating the friction cone, the cone complementary problems (CCP) theory is used to describe the spatial frictional continuous contact problems such that the spatial friction force can be evaluated accurately. A prediction term is introduced to make the established CCP model be applicable to the cases at high sliding speed. To improve the convergence rate of Newton iterations, the velocity variation of the nonsmooth dynamics equations is decomposed into the smooth velocities and nonsmooth (jump) velocities. The smooth velocities are computed by using the generalized-
$\mathbf{a}$
algorithm, and the nonsmooth velocities are integrated via the implicit Euler algorithm. The accelerated projected gradient descend (APGD) algorithm is used to solve the CCP. Finally, four numerical examples are given to validate the proposed computation methodology.
9 citations
Journal Article•
TL;DR: This thesis proposes a set of Optimal Transport tools and analyzes the mathematical properties of the various proposed tools, establishes algorithmic solutions to compute them and studies their applicability in numerous machine learning scenarii which cover, in particular, classification, simplification, partitioning of structured data, as well as heterogeneous domain adaptation.
Abstract: Le Transport Optimal est une theorie permettant de definir des notions geometriques de distance entre des distributions de probabilite et de trouver des correspondances, des relations, entre des ensembles de points. De cette theorie, a la frontiere entre les mathematiques et l'optimisation, decoule de nombreuses applications en machine learning. Cette these propose d'etudier le scenario, complexe, dans lequel les differentes donnees appartiennent a des espaces incomparables}. En particulier nous abordons les questions suivantes : comment definir et appliquer le transport optimal entre des graphes, entre des donnees structurees ? Comment l'adapter lorsque les donnees sont variees et ne font pas partie d'un meme espace metrique ? Cette these propose un ensemble d'outils de Transport Optimal pour ces differents cas. Un important volet est notamment consacre a l'etude de la distance de Gromov-Wasserstein dont les proprietes permettent de definir d'interessants problemes de transport sur des espaces incomparables. Plus largement, nous analysons les proprietes mathematiques des differents outils proposes, nous etablissons des solutions algorithmiques pour les calculer et nous etudions leur applicabilite dans de nombreux scenarii de machine learning qui couvrent, notamment, la classification, la simplification, le partitionnement de donnees structurees, ainsi que l'adaptation de domaines heterogenes.
9 citations