Author
S. K. Neogy
Other affiliations: Indian Statistical Institute, Delhi Centre
Bio: S. K. Neogy is an academic researcher from Indian Statistical Institute. The author has contributed to research in topic(s): Linear complementarity problem & Complementarity theory. The author has an hindex of 10, co-authored 44 publication(s) receiving 576 citation(s). Previous affiliations of S. K. Neogy include Indian Statistical Institute, Delhi Centre.
Papers
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TL;DR: In this paper, the authors consider the class of the invex functions introduced by Hanson and show that under certain conditions, a function defined on a set of non-invex sets A is pre-quasi-inverse on A.
Abstract: In this paper we consider the class of the invex function introduced by Hanson. We show that under certain condition an invex function defined on an invex set A is preinvex on A. Similarly, a quasiinvex function defined on an invex set A is pre-quasiinvex.
307 citations
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.
37 citations
01 Apr 2008
TL;DR: In this article, the authors present an analysis of sets of Constraints, Traveling Salesman Problem, and Tolerance-Based Algorithms for linear programs with Totally Unimodular Coefficient Matrix Interior Point Method for Convex Quadratic Programming Analysis of Sets of CONstraints.
Abstract: Mathematical Programming and Its Applications in Finance Linear Programs with Totally Unimodular Coefficient Matrix Interior Point Method for Convex Quadratic Programming Analysis of Sets of Constraints, Traveling Salesman Problem and Tolerance-Based Algorithms Pedigree Polytope One-Defective Vertex Coloring Problem Complementarity Problem Fuzzy Twin Support Vector Machines for Pattern Classification Minimum Sum of Absolute Errors Regression Hedging Against the Market with No Short Selling Mathematical Programming and Electrical Network Analysis Dynamic Optimal Control Policy Forecasting for Supply Chain and Portfolio Management Variational Analysis in Bilevel Programming Game Engineering Games of Connectivity Robust Feedback Nash Equilibrium De Facto Delegation and Proposer Rules Bargaining Set in Effectivity Function Dynamic Oligopoly as a Mixed Large Game -- Toy Market, Balanced Games, Market Equilibrium for Combinatorial Auctions and the Matching Core of Non-negative TU Games Continuity, Manifolds and Arrow's Social Choice Problem Mixture Class of Stochastic Games.
20 citations
TL;DR: This paper surveys the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies ofThe players forSpecial cases of nonzero-sum StochasticGames, using finite-step algorithms based on pivoting.
Abstract: In this paper, we survey the recent literature on computing the value vector and the associated optimal strategies of the players for special cases of zero-sum stochastic games, or in computing a Nash equilibrium point and the corresponding stationary strategies of the players for special cases of nonzero-sum stochastic games, using finite-step algorithms based on pivoting. Examples of finite-step pivoting algorithms are the various simplex-type algorithms, such as the primal simplex or dual simplex method for solving the linear programming problem or Lemke's or Lemke-Howson's algorithm for solving the linear complementarity problem. Also included are Lemke-type algorithms for solving various generalisations of the linear complementarity problem. The survey also includes a few new results and observations.
19 citations
TL;DR: In this article, the authors considered positive subdefinite matrices (PSBD) and showed that linear complementarity problems with PSBD matrices of rank ⩾ 2 are processable by Lemke's algorithm and that a PSBD matrix of rank 2 belongs to the class of sufficient matrices introduced by R.W. Cottle et al.
Abstract: In this article, we consider positive subdefinite matrices (PSBD) recently studied by J.-P. Crouzeix et al. [SIAM J. Matrix Anal. Appl. 22 (2000) 66] and show that linear complementarity problems with PSBD matrices of rank ⩾2 are processable by Lemke's algorithm and that a PSBD matrix of rank ⩾2 belongs to the class of sufficient matrices introduced by R.W. Cottle et al. [Linear Algebra Appl. 114/115 (1989) 231]. We also show that if a matrix A is a sum of a merely positive subdefinite copositive plus matrix and a copositive matrix, and a feasibility condition is satisfied, then Lemke's algorithm solves LCP( q , A ). This supplements the results of Jones and Evers.
17 citations
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TL;DR: A novel classification framework is proposed that provides a full picture of current literature on where and how BDA has been applied within the SCM context and reveals a number of research gaps, which leads to future research directions.
Abstract: The rapid growing interest from both academics and practitioners towards the application of Big Data Analytics (BDA) in Supply Chain Management (SCM) has urged the need of review up-to-date research development in order to develop new agenda. This review responds to this call by proposing a novel classification framework that provides a full picture of current literature on where and how BDA has been applied within the SCM context. The classification framework is structured based on the content analysis method of Mayring (2008), addressing four research questions on (1) what areas of SCM that BDA is being applied, (2) what level of analytics is BDA used in these application areas, (3) what types of BDA models are used, and finally (4) what BDA techniques are employed to develop these models. The discussion tackling these four questions reveals a number of research gaps, which leads to future research directions.
193 citations
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.
185 citations
TL;DR: In this article, several kinds of invariant monotone maps and generalized invariant maps are introduced, and relations between generalized monotonicity and generalized invexity are established, which are generalizations of those presented by Karamardian and Schaible.
Abstract: In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results are generalizations of those presented by Karamardian and Schaible.
122 citations
TL;DR: In this article, a characterization of a preinvex function in terms of its relationship with an intermediate-point pre-vexity and prequasi-inveXity is provided.
Abstract: We consider in this paper the class of preinvex functions introduced by T. Weir and co-workers (1988, J. Math. Anal. Appl.136, 29–38; 1988, Bull. Austral. Math. Soc.38, 177–189). Under semi-continuity conditions, a determination of the satisfaction of preinvexity for a function can be achieved via an intermediate-point preinvexity check. A characterization of a preinvex function in terms of its relationship with an intermediate-point preinvexity and prequasi-invexity is provided.
118 citations
TL;DR: This study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems and Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.
Abstract: We address a vendor-managed inventory-routing problem where a supplier (vendor) receives a given amount of a single product each period and distributes it to multiple retailers over a finite time horizon using a capacitated vehicle. Each retailer faces external dynamic demand and is controlled by a deterministic order-up-to level policy requiring that the supplier raise the retailer's inventory level to a predetermined maximum in each replenishment. The problem is deciding on when and in what sequence to visit the retailers such that systemwide inventory holding and routing costs are minimized. We propose a branch-and-cut algorithm and a heuristic based on an a priori tour using a strong formulation. To the best of our knowledge, this study is the first to consider a strong formulation for the inventory replenishment part of inventory-routing problems. Computational results reveal that the new branch-and-cut algorithm and heuristic perform better than those noted in the literature.
98 citations