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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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Journal ArticleDOI
TL;DR: A new direct method for the solution of a BLCP, that is, a linear complementarity problem (LCP) with upper bounds, when its matrix is a symmetric or an unsymmetricP-matrix.
Abstract: In this paper, the authors develop a new direct method for the solution of a BLCP, that is, a linear complementarity problem (LCP) with upper bounds, when its matrix is a symmetric or an unsymmetricP-matrix. The convergence of the algorithm is established by extending Murty's principal pivoting method to an LCP which is equivalent to the BLCP. Computational experience with large-scale BLCPs shows that the basic-set method can solve efficiently large-scale BLCPs with a symmetric or an unsymmetricP-matrix.

14 citations

Journal ArticleDOI

13 citations


Additional excerpts

  • ...and { MBk = 1 α (DB − βLBk ) NBk = 1 α [(1 − α)DB + (α − β)LBk + αUBk ] (12)...

    [...]

  • ...,l} be the MMAOR of (A,B) in (11) to (12) and let Ω, A and B satisfy the assumptions of Theorem 2....

    [...]

Proceedings ArticleDOI
09 Aug 2021
TL;DR: In this paper, the authors provide mathematical details about formulating contact as a complementarity problem in rigid body and soft body animations, and present a range of numerical techniques for solving the associated LCPs and NCPs.
Abstract: Efficient simulation of contact is of interest for numerous physics-based animation applications. For instance, virtual reality training, video games, rapid digital prototyping, and robotics simulation are all examples of applications that involve contact modeling and simulation. However, despite its extensive use in modern computer graphics, contact simulation remains one of the most challenging problems in physics-based animation. This course covers fundamental topics on the nature of contact modeling and simulation for computer graphics. Specifically, we provide mathematical details about formulating contact as a complementarity problem in rigid body and soft body animations. We briefly cover several approaches for contact generation using discrete collision detection. Then, we present a range of numerical techniques for solving the associated LCPs and NCPs. The advantages and disadvantages of each technique are further discussed in a practical manner, and best practices for implementation are discussed. Finally, we conclude the course with several advanced topics, such as anisotropic friction modeling and proximal operators. Programming examples are provided on the course website to accompany the course notes.

13 citations

Journal ArticleDOI
TL;DR: This work studies the structure of this problem and its relationship with the nearest point problem in a pos cone through the concept of polar cones, and designs an efficient algorithm for solving the problem, and carries out computational experiments to evaluate its effectiveness.
Abstract: We consider the problem of finding the nearest point in a polyhedral cone C={x?R n :D x?0} to a given point b?R n , where D?R m×n . This problem can be formulated as a convex quadratic programming problem with special structure. We study the structure of this problem and its relationship with the nearest point problem in a pos cone through the concept of polar cones. We then use this relationship to design an efficient algorithm for solving the problem, and carry out computational experiments to evaluate its effectiveness. Our computational results show that our proposed algorithm is more efficient than other existing algorithms for solving this problem.

13 citations

Journal ArticleDOI
TL;DR: In this article, a new error bound for the linear complementarity problem is given when the involved matrix is a $B$-matrix, and it is shown that this bound improves the corresponding result in [M. Garc\'{i}a-Esnaola and J.M. Li.
Abstract: A new error bound for the linear complementarity problem is given when the involved matrix is a $B$-matrix. It is shown that this bound improves the corresponding result in [M. Garc\'{i}a-Esnaola and J.M. Pe\~{n}a. Error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 22:1071--1075, 2009.] in some cases, and that it is sharper than that in [C.Q. Li and Y.T. Li. Note on error bounds for linear complementarity problems for $B$-matrices. {\em Appl. Math. Lett.}, 57:108--113, 2016.].

13 citations