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A. K. Das

Bio: A. K. Das is an academic researcher from Indian Statistical Institute. The author has contributed to research in topics: Linear complementarity problem & Complementarity theory. The author has an hindex of 8, co-authored 41 publications receiving 180 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.

27 citations

Journal ArticleDOI
TL;DR: It is shown that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$Q0-property is captured by sufficient matrices introduced by Cottle et al.
Abstract: In this article, we study the properties of some matrix classes using principal pivot transform (PPT). These matrices with some additional conditions have nonnegative principal minors. We show that a subclass of almost fully copositive matrices intorduced in (Linear Algebra Appl 400:243–252 2005) with $$Q_{0}$$ -property is captured by sufficient matrices introduced by Cottle et al. in (Linear Algebra Appl 114/115:231–249 1989) and the solution set of a linear complementarity problem is the same as the set of Karush–Kuhn–Tucker stationary points of the corresponding quadratic programming problem. We introduce some more PPT based matrix classes in continuation of (Linear Algebra Appl 400:243–252 2005) and study the properties of these classes.

27 citations

Journal ArticleDOI
TL;DR: This special issue of the Annals of Operations Research contains selected and refereed papers on the topic optimization models with economic and game theoretic applications, presented at the International Symposium on Applied Optimization and Game Theoretic Models held during January 9–11, 2013.
Abstract: Optimization models have a wide range of applications in economics and game theory. This special issue of the Annals of Operations Research contains selected and refereed papers on the topic optimization models with economic and game theoretic applications. Most of the papers in this special issue were presented at the International Symposium on Applied Optimization and Game Theoretic Models (ISAOGTM13) held during January 9–11, 2013, at the Indian Statistical Institute, Delhi Centre. This International Symposiumwas designed to promote research and applications in applied optimization and game theory by bringing together leading experts and other specialists in the field around the world with young scholars. This symposium mainly focused on classical and modern optimization theory, algorithms (local and global aspects), stochastic optimization, structured optimization, as well as related topics in applied mathematics that contain applications of optimization models in economics and game theory. Around 120 participants including speakers participated in this symposium. This symposium was an event under the project optimization and reliability modeling funded by the Indian Statistical Institute. Having broad international appeal it provided an excellent opportunity to disseminate the latest major achievements and to explore new directions and perspectives, dealingwith topics of fundamental importance in applied optimization and other related sciences (economics, physics, engineering). A special session titled Professor Santosh N. Kabadi Memorial Session was organized on combinatorial optimization to recall the memory of our dear friend Professor Santosh N. Kabadi, University of New

27 citations

Journal ArticleDOI
TL;DR: The concept of principal pivot transform and its generalization in the context of vertical linear complementarity problem is revisited and an application of generalized principal pivottransform in game theory is presented.
Abstract: In this article, we revisit the concept of principal pivot transform and its generalization in the context of vertical linear complementarity problem. We study solution set and solution rays of a vertical linear complementarity problem. Finally we present an application of generalized principal pivot transform in game theory.

23 citations

Journal ArticleDOI
01 Dec 2019-Opsearch
TL;DR: The proposed algorithm can process LCP (q, A) in polynomial time under some assumptions and is observed to be able to process the solution aspects of linear complementarity problem with hidden Z-matrix.
Abstract: We propose an interior point method to compute solution of linear complementarity problem LCP (q, A) given that A is a real square hidden Z-matrix (generalization of Z-matrix) and q is a real vector. The class of hidden Z-matrix is important in the context of mathematical programming and game theory. We study the solution aspects of linear complementarity problem with $$A \in$$ hidden Z-matrix. We observe that our proposed algorithm can process LCP (q, A) in polynomial time under some assumptions. Two numerical examples are illustrated to support our result.

23 citations


Cited by
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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

13,333 citations

Journal ArticleDOI
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.

329 citations

Journal ArticleDOI
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

Journal ArticleDOI
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.

107 citations

Journal ArticleDOI
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.

95 citations