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R. Sridhar

Bio: R. Sridhar is an academic researcher from Indira Gandhi Institute of Development Research. The author has contributed to research in topics: Linear complementarity problem & Complementarity theory. The author has an hindex of 1, co-authored 2 publications receiving 38 citations.

Papers
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Journal ArticleDOI
TL;DR: This paper forms this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke, and shows that the class of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as theclass of equivalent square matrices in Lemke's algorithm.
Abstract: Given a vertical block matrixA, we consider in this paper the generalized linear complementarity problem VLCP(q, A) introduced by Cottle and Dantzig. We formulate this problem as a linear complementarity problem with a square matrixM, a formulation which is different from a similar formulation given earlier by Lemke. Our formulation helps in extending many well-known results in linear complementarity to the generalized linear complementarity problem. We also show that the class of vertical block matrices which Cottle and Dantzig's algorithm can process is the same as the class of equivalent square matrices which Lemke's algorithm can process. We also present some degree-theoretic results on a vertical block matrix.

43 citations

Journal ArticleDOI
TL;DR: A new class of matrices is defined and it is established that in$$\bar Z$$ superfluous matrices of any ordern ⩾ 4 can easily be constructed.
Abstract: Superfluous matrices were introduced by Howe (1983) in linear complementarity. In general, producing examples of this class is tedious (a few examples can be found in Chapter 6 of Cottle, Pang and Stone (1992)). To overcome this problem, we define a new class of matrices\(\bar Z\) and establish that in\(\bar Z\) superfluous matrices of any ordern ⩾ 4 can easily be constructed. For every integerk, an example of a superfluous matrix of degreek is exhibited in the end.

1 citations


Cited by
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Journal ArticleDOI
TL;DR: The method described, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on data that can be fit well by a convex function.
Abstract: We consider the problem of fitting a convex piecewise-linear function, with some specified form, to given multi-dimensional data. Except for a few special cases, this problem is hard to solve exactly, so we focus on heuristic methods that find locally optimal fits. The method we describe, which is a variation on the K-means algorithm for clustering, seems to work well in practice, at least on data that can be fit well by a convex function. We focus on the simplest function form, a maximum of a fixed number of affine functions, and then show how the methods extend to a more general form.

220 citations

Journal ArticleDOI
TL;DR: A non-interior continuation method for solving generalized linear complementarity problems (GLCP) introduced by Cottle and Dantzig is proposed, based on a smoothing function derived from the exponential penalty function first introduced by Kort and Bertsekas for constrained minimization.
Abstract: In this paper, we propose a non-interior continuation method for solving generalized linear complementarity problems (GLCP) introduced by Cottle and Dantzig. The method is based on a smoothing function derived from the exponential penalty function first introduced by Kort and Bertsekas for constrained minimization. This smoothing function can also be viewed as a natural extension of Chen-Mangasarian’s neural network smooth function. By using the smoothing function, we approximate GLCP as a family of parameterized smooth equations. An algorithm is presented to follow the smoothing path. Under suitable assumptions, it is shown that the algorithm is globally convergent and local Q-quadratically convergent. Few preliminary numerical results are also reported.

71 citations

Journal ArticleDOI
TL;DR: It is proved that every accumulation point of this sequence is a solution of EVLCP(M, q) under the assumption of row ${\cal W}_0$-property, and if row W-property holds at the solution point, then the convergence rate is quadratic.
Abstract: In this paper, we reformulate the extended vertical linear complementarity problem (EVLCP(m,q)) as a nonsmooth equation H(t,x)=0, where $H: \mbox{\smallBbb R}^{n+1} \to \mbox{\smallBbb R}^{n+1}$, $t \in \mbox{\smallBbb R}$ is a parameter variable, and $x \in \mbox{\smallBbb R}$ is the original variable. H is continuously differentiable except at such points (t,x) with t=0. Furthermore H is strongly semismooth. The reformulation of EVLCP(m, q) as a nonsmooth equation is based on the so-called aggregation (smoothing) function. As a result, a Newton-type method is proposed which generates a sequence {wk=(tk,xk)} with all tk >0. We prove that every accumulation point of this sequence is a solution of EVLCP(M, q) under the assumption of row ${\cal W}_0$-property. If row ${\cal W}$-property holds at the solution point, then the convergence rate is quadratic. Promising numerical results are also presented.

61 citations

Journal ArticleDOI
TL;DR: Using the topological degree and the concept of exceptional family of elements for a continuous function, this work proves a very general existence theorem for the nonlinear complementarity problem.
Abstract: Using the topological degree and the concept of exceptional family of elements for a continuous function, we prove a very general existence theorem for the nonlinear complementarity problem. This result is an alternative theorem. A generalization of Karamardian‘s condition and the asymptotic monotonicity are also introduced. Several applications of the main results are presented.

39 citations

Journal ArticleDOI
TL;DR: It is shown that the Extended Linear Complementarity Problem (ELCP) can be recast as a standard Linear Complementation Problem (LCP) provided that the surplus variables or the feasible set of the ELCP are bounded.

27 citations