Author

# A. K. Das

Bio: A. K. Das 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 8, co-authored 41 publication(s) receiving 180 citation(s).

##### Papers

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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

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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: In this paper, the authors considered the class C 0 f of fully copositive matrices and the class E 0f of fully semimonotone matrices, and they showed that the columns of these matrices with positive diagonal entries are column sufficient.

Abstract: In this paper we consider the class C 0 f of fully copositive and the class E 0 f of fully semimonotone matrices. We show that C 0 f matrices with positive diagonal entries are column sufficient. We settle a conjecture made by Murthy and Parthasarathy to the effect that a C 0 f ∩ Q 0 matrix is positive semidefinite by providing a counterexample. We finally consider E 0 f matrices introduced by Cottle and Stone (Math. Program. 27 (1983) 191–213) and partially address Stone's conjecture to the effect that E 0 f ∩ Q 0 ⊆ P 0 by showing that E 0 f ∩ D c matrices are P 0 , where D c is the Doverspike class of matrices.

13 citations

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TL;DR: It is shown that for a subclass of GPSBD matrices, the solution set of a linear complementarity problem is same as the set of Karush--Kuhn--Tucker-stationary points of the corresponding quadratic programming problem.

Abstract: The class of generalized positive subdefinite (GPSBD) matrices is an interesting matrix class introduced by Crouzeix and Komlosi [Appl. Optim. 59, Kluwer, Dordrecht, The Netherlands, 2001, pp. 45-63]. In this paper, we obtain some properties of GPSBD matrices. We show that copositive GPSBD matrices are $P_{0}$ and a merely generalized positive subdefinite (MGPSBD) matrix with some additional conditions belongs to the class of row sufficient matrices introduced by Cottle, Pang, and Venkateswarn [Linear Algebra Appl., 114/115 (1989), pp. 231-249]. Further, it is shown that for a subclass of GPSBD matrices, the solution set of a linear complementarity problem is same as the set of Karush--Kuhn--Tucker-stationary points of the corresponding quadratic programming problem. We provide a counter example to show that a copositive GPSBD matrix need not be sufficient in general. Finally, we show that if a matrix $A$ can be written as a sum of a copositive-plus MGPSBD matrix with an additional condition and a copositive matrix and if it satisfies a feasibility condition, then Lemke's algorithm can solve LCP$(q,A).$ This further extends the applicability of Lemke's algorithm and a result of Evers.

11 citations

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TL;DR: In this article, Ravindran et al. introduced a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost n 0 -matrices) and obtained a sufficient condition for this class to hold Q-property.

Abstract: In this article, we introduce a new matrix class almost (a subclass of almost N 0-matrices which are obtained as a limit of a sequence of almost N-matrices) and obtain a sufficient condition for this class to hold Q-property. We produce a counter example to show that an almost -matrix need not be a R 0-matrix. We also introduce another two new limiting matrix classes, namely of exact order 2, for a positive vector d and prove sufficient conditions for these classes to satisfy Q-property. Murthy et al. [Murthy, G.S.R., Parthasarathy, T. and Ravindran, G., 1993, A copositive Q-matrix which is not R 0. Mathematical Programming, 61, 131–135.] showed that Pang's conjecture ( ) is not true even when E 0 is replaced by C 0. We show that Pang's conjecture is true if E 0 is replaced by almost C 0 Finally, we present a game theoretic proof of necessary and sufficient conditions of an almost P 0-matrix satisfying Q-property.

10 citations

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TL;DR: This book by a teacher of statistics (as well as a consultant for "experimenters") is a comprehensive study of the philosophical background for the statistical design of experiment.

Abstract: THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

12,326 citations

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TL;DR: Incomplete Factorials, Fractional Replication, Intermediate Factorial, and Nested Designs as discussed by the authors are some of the examples of incomplete Factorial Experiments and incomplete fractional replicates.

Abstract: Introduction. Simple Comparison Experiments. Two Factors, Each at Two Levels. Two Factors, Each at Three Levels. Unreplicated Three--Factor, Two--Level Experiments. Unreplicated Four--Factor, Two--Level Experiments. Three Five--Factor, Two--Level Unreplicated Experiments. Larger Two--Way Layouts. The Size of Industrial Experiments. Blocking Factorial Experiments, Fractional Replication--Elementary. Fractional Replication--Intermediate. Incomplete Factorials. Sequences of Fractional Replicates. Trend--Robust Plans. Nested Designs. Conclusions and Apologies.

252 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

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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

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TL;DR: A new multi-class classification algorithm, called Twin-KSVC, is proposed in this paper, which takes the advantages of both TSVM and K-SVCR and evaluates all the training points into a “1-versus-1-Versus-rest” structure, so it generates ternary outputs.

Abstract: Twin support vector machine (TSVM) is a novel machine learning algorithm, which aims at finding two nonparallel planes for each class. In order to do so, one needs to resolve a pair of smaller-sized quadratic programming problems rather than a single large one. Classical TSVM is proposed for the binary classification problem. However, multi-class classification problem is often met in our real world. For this problem, a new multi-class classification algorithm, called Twin-KSVC, is proposed in this paper. It takes the advantages of both TSVM and K-SVCR (support vector classification-regression machine for k-class classification) and evaluates all the training points into a “1-versus-1-versus-rest” structure, so it generates ternary outputs { −1, 0, +1}. As all the samples are utilized in constructing the classification hyper-plane, our proposed algorithm yields higher classification accuracy in comparison with other two algorithms. Experimental results on eleven benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.

82 citations