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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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TL;DR: In this paper, it was shown that within the class of column adequate matrices, a matrix is in ''Pnot'' if and only if it is completely ''Qnot'' (i) completely ''Cnotf'' (cnotf$)-matrices introduced by Murthy and Parthasarathy [SIAM J. Matrix Anal. Appl.
Abstract: In this article we present some recent results on the linear complementarity problem. It is shown that (i) within the class of column adequate matrices, a matrix is in $\Qnot$ if and only if it is completely $\Qnot$ (ii) for the class of $\Cnotf$-matrices introduced by Murthy and Parthasarathy [SIAM J. Matrix Anal. Appl., 16 (1995), pp. 1268--1286], we provide a sufficient condition under which a matrix is in $\Pnot$ and as a corollary of this result, we give an alternative proof of the result that $\Cnotf \cap \Qnot \sset \Pnot$ (iii) within the class of INS-matrices introduced by Stone [Department of Operations Research, Stanford University, Stanford, CA, 1981], a nondegenerate matrix must necessarily have the block property introduced by Murthy, Parthasarathy, and Sriparna [G. S. R. Murthy, T. Parthasarathy, and B. Sriparna, Linear Algebra Appl., 252 (1997), pp. 323--337]. Furthermore, we conjecture that if a matrix has block property, then it must be Lipschitzian. This problem is an important one from two angles: if the conjecture is true, it provides a finite test to check whether a given matrix is Lipschitzian or nondegenerate INS; and it settles an open problem posed by Stone. It is shown that the conjecture is true in the cases of 2 x 2-matrices, nonnegative and nonpositive matrices of general order.
8 citations
Cites background from "Linear complementarity, linear and ..."
...LCP has numerous applications, both in theory and in practice, and is treated by a vast literature (see [2, 10])....
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...204 of [10])....
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...This is because, if B has this property, then Graves’s algorithm processes (q,B) for any q and terminates either with a solution or with the conclusion that F (q,B) = ∅ (see Chapter 4 of [10] and Theorem 3....
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01 Jan 2010
TL;DR: The robustness of the IPSPRT and dynamic sensor selection algorithm to common wireless sensor networking errors and failures is evaluated using the carbon sequestration site monitoring application as a case study.
Abstract: This dissertation concerns the sequential large-scale detection of multiple potential sources using wireless sensor networks. A new 2-step approach to sequential multiple-source detection is introduced called the iterative partial sequential probability ratio test (IPSPRT) that minimizes the time-to-decision as the desired probability of false alarm and probability of miss decrease. The first step of the IPSPRT sequentially decides whether any or no sources become active at a specific time, based on a sequential probability ratio test using the generalized likelihood ratio such that the probability of indecision is minimized and the maximum probability of false alarm and maximum probability of miss are bounded. If step one decides that some source is active, step two identifies active sources through an iterative maximization of the likelihood ratio and physical inspection process such that the probability that an active source is not detected is bounded. After a decision is made regarding sources which become active at a specific time, the IPSPRT increments the time at which sources are hypothesized to become active and the procedure continues. Numerical evaluations of the IPSPRT are provided in comparison to other feasible methods for a diffusion process monitoring example consisting of 100 sensors and 100 potential sources. A new dynamic sensor selection problem is formulated for the non-Bayesian multiple source detection problem using a generalized likelihood ratio based dynamic sensor selection strategy (GLRDSS) which a minimum number of sensors to report observations at each sampling instance. An evaluation of the GLRDSS is provided through simulation. A carbon sequestration site monitoring application is introduced as a case study and a test bed implementation discussed. The robustness of the IPSPRT and dynamic sensor selection algorithm to common wireless sensor networking errors and failures is evaluated using the carbon sequestration site monitoring application as a case study.
8 citations
01 Jan 1991
TL;DR: In this article, a GAUSS program that can be used to find equilibria for applied general equilibrium models, and fix-price equilibrium for general non-Walrasian mOdels is presented.
Abstract: This paper contains a GAUSS program that can be used, among other things, to find equilibria for applied general equilibrium models, and fix-price equilibria for general non-Walrasian mOdels . Simple applications of these two cases, as well as to linear and quadratic programming, are also provided . *This work represents the first stage of research in progress, kindly supported by Mexico's Secretaria de Comercio y Fomento Industrial, on the effects of changes in tariffs for economies with price rigidities. The program contained in this paper can be freely used for teaching , research, or any other noncommercial purpose.
8 citations
Cites background or methods from "Linear complementarity, linear and ..."
...It is worth ' .lting out, however, that Lemke's method is not the only procedure available ( s ee , e . g., Murty's, 1974, and the references in Murty, 1988)....
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...F ' r more applications of the linear complementarity problem, see the delight : ul book by Murty (1988)....
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..., Murty, 1988, Chap....
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TL;DR: A new error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix and this bound improves existing results.
Abstract: A new error bound for the linear complementarity problem is obtained when the involved matrix is a B-matrix. This bound improves existing results. Finally, two numerical examples are also g...
8 citations
TL;DR: This paper solves an equivalent mixed integer linear programming formulation of the original binary-constrained mixed, linear complementarity problem (with a smaller number of complementarity constraints) to guarantee a solution to the problem.
8 citations
Cites background from "Linear complementarity, linear and ..."
...[5] S.C. Billups & K.G. Murty (2000), Complementarity problems....
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...[29] K.G. Murty (1988), Linear complementarity, linear and nonlinear programming....
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