Book•
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 2016
TL;DR: In this paper, the authors investigated the appropriateness of modeling the human ankle joint based on a stationary axis of rotation and a technique is also proposed which is capable of predicting the directional changes of the ankle axis during the foot flexion.
Abstract: This thesis contains contributions to contact simulation and human motion analysis. Effects of the foot and ankle modelling techniques on the foot kinematics and dynamics are investigated. The analyses are carried out based on experimental data obtained using a motion capture system. The appropriateness of modelling the human ankle joint based on a stationary axis of rotation is investigated and a technique is also proposed which is capable of predicting the directional changes of the ankle axis during the foot flexion. Furthermore, two main modelling assumptions related to the number of the foot segments and the dimension of the foot model were the subject of the foot dynamics analyses. Effects of these modelling assumptions on the ankle joint torque and power are determined. A framework was developed which quantifies the gait abnormality of multiple sclerosis (MS) patients using a Kinect camera. The reliability of such a framework in assessing gait parameters in MS patients is evaluated based on captured data by Kinect. Also, a novel set of MS gait indices based on the concept of dynamic time warping is introduced whichcan characterize a patient's gait pattern and quantify the subject's gait deviation from the healthy population. In the second part of the thesis, two algorithms, namely, the accelerated-box and the generalized inverse-based algorithms, were developed for contact dynamics simulation. The accelerated-box algorithm improves the simulation of rigid body contact problems, in particular when the system under consideration has redundant constraints. The mathematical formulation is expressed in terms of a mixed linear complementarity problem (MLCP). The accelerated-box approach is partly motivated by the box friction model which is one of the existing approaches to solve contact problems. The original box friction model suffers from certain drawbacks in the presence of a large number of contact points such as long computational time, divergence problems, and instability. On the other hand, the accelerated-box approach developed in this thesis overcomes such drawbacks by taking advantage of the sparse structure of the lead matrix of the MLCP. This new method reduces the sensitivity of the solution to the constraint relaxation terms and decreases the number of required pivots to obtain the solution, and hence, shorter computational times result. This approach accordingly suggests a more reliable method for real-time simulation of multibody systems. A method based on the use of the Moore-Penrose generalized inverse was developed to deal with systems with redundant contacts. This approach omits the necessity of relaxing the constraints when redundancy exists in the system. To develop such a method, the generalized inverse is incorporated inside the pivoting steps of the MLCP solver. The method is very stable and robust, and its computational time is considerably smaller than the counterpartmethods, specially for highly redundant systems. Finally, a novel complementarity problem formulation is introduced. In…
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Cites background or methods from "Linear complementarity, linear and ..."
...It can be shown that if an LCP is solvable, it will have at least a solution at one of the vertices of such a polytope [116]....
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...Regardless of how the LCP is formulated, for the solution, a well-known category of approaches is based on the so-called symplex methods, which are known as the direct or pivoting methods as well [48, 116, 89]....
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...Moreover, if the lead matrix of an LCP is a P-Matrix, block pivoting algorithms will converge to the solution [116]....
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18 Apr 2013
TL;DR: A method using subdivision technique to approximate the whole Pareto-optimal set of the linearly constrained, convex multi objective optimization problem, and some technique to find joint decreasing direction for unconstrained and linear constrained case are proposed.
Abstract: In multi objective optimization problems several objective functions have to be minimized simultaneously. In this work, we present a new computational method for the numerical solution of the linearly constrained, convex multi objective optimization problem. We propose some technique to find joint decreasing direction for unconstrained and linearly constrained case as well. Based on these results we introduce a method using subdivision technique to approximate the whole Pareto-optimal set of the linearly constrained, convex multi objective optimization problem. Finally, we illustrate computations of our algorithm by solving the Markowitz-model on real data.
1 citations
TL;DR: By extending the classical Newton method, the generalized Newton method (GNM) with high-order convergence for solving a class of large-scale linear complementarity problems, which is based on an additional parameter and a modulus-based nonlinear function is presented.
Abstract: In this paper, by extending the classical Newton method, we present the generalized Newton method (GNM) with high-order convergence for solving a class of large-scale linear complementarity problems, which is based on an additional parameter and a modulus-based nonlinear function. Theoretically, the performance of high-order convergence is analyzed in detail. Some numerical experiments further demonstrate the efficiency of the proposed new method.
1 citations
Additional excerpts
...2 Initials z0 (1) z 0 (1) z 0 (2) z 0 (2) Methods GNIM FBSN GNIM FBSN n = 500 It 2 11 3 11 CPU 0....
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...1 Initials z0 (1) z 0 (1) z 0 (2) z 0 (2) Methods GNIM FBSN GNIM FBSN n = 500 It 2 11 3 11 CPU 0....
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...1 Initials z0 (1) z 0 (1) z 0 (2) z 0 (2) Methods GNIM CBSN GNIM CBSN n = 50 It 2 3 3 4 CPU 0....
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Dissertation•
01 Jan 2012
TL;DR: In this paper, a new class of complementarity problems, known as absolute complementarity problem is introduced and investigated, and several iterative methods including the minimization technique, residual method and homotopy perturbation method are suggested and analyzed.
Abstract: It is well known that a wide class of problems, which arises in pure and applied sciences can be studied in the unified frame work of the system of absolute value equations of the type Ax − x = b,, n n A R × I . n bIR Here x is the vector in n R with absolute values of components of x.In this thesis, several iterative methods including the minimization technique, residual method and homotopy perturbation method are suggested and analyzed.Convergence analysis of these new iterative methods is considered under suitable conditions.Several special cases are discussed.Numerical examples are given to illustrate the implementation and efficiency of these methods.Comparison with other methods shows that these new methods perform better.A new class of complementarity problems, known as absolute complementarity problem is introduced and investigated.Existence of a unique solution of the absolute complementarity problem is proved.A generalized AOR method is proposed.The convergence of GAOR method is studied.It is shown that the absolute complementarity problem includes system of absolute value equations and related optimizations as special cases.
1 citations
24 Jul 2016
TL;DR: This paper presents a methodology for the generation of a Fuzzy Inference System (FIS) for multivariate time series forecasting from historical data, aiming at good performance in both forecasting accuracy and rule base interpretability - in order to extract knowledge about the relationship between the modeled time series.
Abstract: A time series is the most commonly used representation for the evolution of a given variable over time. In a time series forecasting problem, a model aims at predicting the series' future values, assuming that all information needed to do so is contained in the series' past behavior. Since the phenomena described by the time series does not always exist in isolation, it is possible to enhance the model with historical data from other related time series. The structure formed by several different time series occurring in parallel, each featuring the same interval and dimension, is called a multivariate time series. This paper presents a methodology for the generation of a Fuzzy Inference System (FIS) for multivariate time series forecasting from historical data, aiming at good performance in both forecasting accuracy and rule base interpretability - in order to extract knowledge about the relationship between the modeled time series. Several aspects related to the operation and construction of such a FIS are investigated regarding complexity and semantic clarity. The model is evaluated by applying it to multivariate time series obtained from the complete M3 competition database and by comparing it to other methods in terms of accuracy. In addition knowledge extraction possibilities from the resulting rule base are explored.
1 citations
Cites methods from "Linear complementarity, linear and ..."
...AutoMFIS uses the active set method [15], with a...
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