			Home About us Contact

Linear Complementarity Problem (linear + complementarity_problem)

Distribution by Scientific Domains

Engineering	71%

Selected Abstracts

A time-stepping method for stiff multibody dynamics with contact and friction,

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2002
Mihai Anitescu
Abstract We define a time-stepping procedure to integrate the equations of motion of stiff multibody dynamics with contact and friction. The friction and non-interpenetration constraints are modelled by complementarity equations. Stiffness is accommodated by a technique motivated by a linearly implicit Euler method. We show that the main subproblem, a linear complementarity problem, is consistent for a sufficiently small time step h. In addition, we prove that for the most common type of stiff forces encountered in rigid body dynamics, where a damping or elastic force is applied between two points of the system, the method is well defined for any time step h. We show that the method is stable in the stiff limit, unconditionally with respect to the damping parameters, near the equilibrium points of the springs. The integration step approaches, in the stiff limit, the integration step for a system where the stiff forces have been replaced by corresponding joint constraints. Simulations for one- and two-dimensional examples demonstrate the stable behaviour of the method. Published in 2002 by John Wiley & Sons, Ltd. [source]

Models of non-smooth switches in electrical systems

INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, Issue 3 2005
Christoph Glocker
Abstract Idealized modelling of diodes, relays and switches in the framework of linear complementarity is introduced. Within the charge approach, the classical electromechanical analogy is extended to passively and actively switching components in electrical circuits. The associated branch relations are expressed in terms of set-valued functions, which allow to formulate the circuit's dynamic behaviour as a differential inclusion. This approach is demonstrated by the example of the DC,DC buck converter. A difference scheme, known in mechanics as time stepping, is applied for numerical approximation of the evolution problem. The discretized inclusions are formulated as a linear complementarity problem in standard form, which implicitly takes care of all switching events by its solution. State reduction, which requires manipulation of the set-valued branch relations in order to obtain a minimal model, is performed on the example of the buck converter. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Neural network approach to firm grip in the presence of small slips

JOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2001
A. M. Al-Fahed Nuseirat
This paper presents a two stage method for constructing a firm grip that can tolerate small slips of the fingertips. The fingers are assumed to be of frictionless contact type. The first stage was to formulate the interaction in the gripper,object system as a linear complementarity problem (LCP). Then it was solved using a special neural network to find minimal fingers forces. The second stage was to use the obtained results in the first stage as a static mapping in training another neural network. The second neural network training included emulating the slips by random noise in the form of changes in the positions of the contact points relative to the reference coordinate system. This noisy training increased robustness against unexpected changes in fingers positions. Genetic algorithms were used in training the second neural network as global optimization techniques. The resulting neural network is a robust, reliable, and stable controller for rigid bodies that can be handled by a robot gripper. © 2001 John Wiley & Sons, Inc. [source]

A modified modulus method for symmetric positive-definite linear complementarity problems

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2 2009
Jun-Liang Dong
Abstract By reformulating the linear complementarity problem into a new equivalent fixed-point equation, we deduce a modified modulus method, which is a generalization of the classical one. Convergence for this new method and the optima of the parameter involved are analyzed. Then, an inexact iteration process for this new method is presented, which adopts some kind of iterative methods for determining an approximate solution to each system of linear equations involved in the outer iteration. Global convergence for this inexact modulus method and two specific implementations for the inner iterations are discussed. Numerical results show that our new methods are more efficient than the classical one under suitable conditions. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Optimal control of a revenue management system with dynamic pricing facing linear demand

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2006
Fee-Seng Chou
Abstract This paper considers a dynamic pricing problem over a finite horizon where demand for a product is a time-varying linear function of price. It is assumed that at the start of the horizon there is a fixed amount of the product available. The decision problem is to determine the optimal price at each time period in order to maximize the total revenue generated from the sale of the product. In order to obtain structural results we formulate the decision problem as an optimal control problem and solve it using Pontryagin's principle. For those problems which are not easily solvable when formulated as an optimal control problem, we present a simple convergent algorithm based on Pontryagin's principle that involves solving a sequence of very small quadratic programming (QP) problems. We also consider the case where the initial inventory of the product is a decision variable. We then analyse the two-product version of the problem where the linear demand functions are defined in the sense of Bertrand and we again solve the problem using Pontryagin's principle. A special case of the optimal control problem is solved by transforming it into a linear complementarity problem. For the two-product problem we again present a simple algorithm that involves solving a sequence of small QP problems and also consider the case where the initial inventory levels are decision variables. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Numerical valuation of options under Kou's model

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
Jari ToivanenArticle first published online: 6 AUG 200
Numerical methods are developed for pricing European and American options under Kou's jump-diffusion model which assumes the price of the underlying asset to behave like a geometrical Brownian motion with a drift and jumps whose size is log-double-exponentially distributed. The price of a European option is given by a partial integro-differential equation (PIDE) while American options lead to a linear complementarity problem (LCP) with the same operator. Spatial differential operators are discretized using finite differences on nonuniform grids and time stepping is performed using the implicit Rannacher scheme. For the evaluation of the integral term easy to implement recursion formulas are derived which have optimal computational cost. When pricing European options the resulting dense linear systems are solved using a stationary iteration. Also for pricing American options similar iterations can be employed. A numerical experiment demonstrates that the described method is very efficient as accurate option prices can be computed in a few milliseconds on a PC. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]