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.
Citations
More filters
01 Sep 2017
TL;DR: This work uses a new friction model that performs velocity-level multi-contact simulation using impulse decomposition and accurately handle friction at each contact point using contact distribution and frictional impulse solvers, which also account for relative motion.
Abstract: We present an interactive and stable multi-contact dynamic simulation algorithm for rigid bodies. Our approach is based on fast frictional dynamics (FFD) [14], which is designed for large sets of non-convex rigid bodies. We use a new friction model that performs velocity-level multi-contact simulation using impulse decomposition. Moreover, we accurately handle friction at each contact point using contact distribution and frictional impulse solvers, which also account for relative motion. We evaluate our algorithm's performance on many complex multi-body benchmarks with thousands of contacts. In practice, our dynamics simulation algorithm takes a few milliseconds per timestep and exhibits more stable behaviors.
Cites methods from "Linear complementarity, linear and ..."
...Some faster techniques have been proposed based on iterative LCP solvers [21], [11], [6]....
[...]
Journal Article•
06 Sep 2013-World Academy of Science, Engineering and Technology, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering
TL;DR: The algorithm for error estimation of BLCP is given and numerical experiments show that the algorithm is efficient.
Abstract: In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient. Keywords—Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P -matrix, M -matrix.
Cites background from "Linear complementarity, linear and ..."
...The linear complementarity problem is of interest in a wide range of applications such as, free boundary problems [1], a Nash-equilibrium in bimatrix games [2], the interval hull of linear systems of interval equations [3], contact problems with friction [4], optimal stopping in Markov chains [5], circuit simulation [6], linear and quadratic programming [7] and economies with institutional restrictions upon prices [8]....
[...]
TL;DR: This work re-wrote the Linear Complementarity Problem in a formulation based on unknown projector operators that allows the introduction of a concept of “stability” that, in a certain way, might explain the way block pivotal algorithm performs.
Cites background from "Linear complementarity, linear and ..."
...Cycling examples of the BPA with P matrices have been constructed [6,1]....
[...]
...The first and to our best knowledge the only monograph completely dedicated to this problem is by Murty [1]....
[...]
Dissertation•
03 Apr 2013
TL;DR: An efficient local incremental re ranking model (LIR), which combines a top-down method with a local reranking model for each sub-problem, and improves the accuracy by absorbing the local category dependencies of sub-problems, which alleviate the errors of top- down method in the higher levels of the hierarchy.
Abstract: Current hierarchical text categorization (HTC) methods mainly fall into three directions: (1) Flat one-vs.-all approach, which flattens the hierarchy into independent nodes and trains a binary one-vs.-all classifier for each node. (2) Top-down method, which uses the hierarchical structure to decompose the entire problem into a set of smaller sub-problems, and deals with such sub-problems in top-down fashion along the hierarchy. (3) Big-bang approach, which learns a single (but generally complex) global model for the class hierarchy as a whole with a single run of the learning algorithm.
These methods were shown to provide relatively high performance in previous evaluations. However, they still suffer from two main drawbacks: (1) relatively low accuracy as they disregard category dependencies, or (2) low computational efficiency when considering such dependencies.
In order to build an accurate and efficient model we adopted the following strategy: first, we design advanced global reranking models (GR) that exploit structural dependencies in hierarchical multi-label text classification (TC). They are based on two algorithms: (1) to generate the k-best classification of hypotheses based on decision probabilities of the flat one-vs.-all and top-down methods; and (2) to encode dependencies in the reranker by: (i) modeling hypotheses as trees derived by the hierarchy itself and (ii) applying tree kernels (TK) to them. Such TK-based reranker selects the best hierarchical test hypothesis, which is naturally represented as a labeled tree. Additionally, to better investigate the role of category relationships, we consider two interesting cases: (i) traditional schemes in which node-fathers include all the documents of their child-categories; and (ii) more general schemes, in which children can include documents not belonging to their fathers.
Second, we propose an efficient local incremental reranking model (LIR), which combines a top-down method with a local reranking model for each sub-problem. These local rerankers improve the accuracy by absorbing the local category dependencies of sub-problems, which alleviate the errors of top-down method in the higher levels of the hierarchy. The application of LIR recursively deals with the sub-problems by applying the corresponding local rerankers in top-down fashion, resulting in high efficiency.
In addition, we further optimize LIR by (i) improving the top-down method by creating local dictionaries for each sub-problem; (ii) using LIBLINEAR instead of LIBSVM; and (iii) adopting the compact representation of hypotheses for learning the local reranking model. This makes LIR applicable for large-scale hierarchical text categorization.
The experimentation on different hierarchical datasets has shown promising enhancements by exploiting the structural dependencies in large-scale hierarchical text categorization.
DOI•
01 Jan 2014TL;DR: Yang et al. as discussed by the authors developed two numerical methods for evaluating option prices under the regime switching model of stock price processes: the Finite Di↵erence lattice method and the Monte Carlo lattice methods.
Abstract: LATTICE METHODS FOR THE VALUATION OF OPTIONS WITH REGIME SWITCHING by Atul Sancheti Hongtao Yang, Examination Committee Chair Associate Professor of Mathematical Science University of Nevada, Las Vegas In this thesis, we have developed two numerical methods for evaluating option prices under the regime switching model of stock price processes: the Finite Di↵erence lattice method and the Monte Carlo lattice method. The Finite Di↵erence lattice method is based on the explicit finite di↵erence scheme for parabolic problems. The Monte Carlo lattice method is based on the simulation of the Markov chain. The advantage of these methods is their flexibility to compute the option prices for any given stock price at any given time. Numerical examples are presented to examine these methods. It has been shown that the proposed methods provides fast and accurate approximations of option prices. Hence they should be helpful for practitioners working in this field.