Author

# Dipti Dubey

Bio: Dipti Dubey is an academic researcher from Indian Statistical Institute. The author has contributed to research in topic(s): Linear complementarity problem & Matrix (mathematics). The author has an hindex of 3, co-authored 9 publication(s) receiving 23 citation(s).

##### Papers

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01 Jan 2018

TL;DR: A Unified Framework for a Class of Mathematical Programming Problems (Dipti Dubey as discussed by the authors ) is a framework for solving a class of problems in graph optimization problems, such as maximizing spectral radius and number of spanning trees in bipartite graphs.

Abstract: Chapter 1. A Unified Framework for a Class of Mathematical Programming Problems (Dipti Dubey).- Chapter 2. Maximizing spectral radius and number of spanning trees in bipartite graphs (Ravindra B. Bapat).- Chapter 3. Optimization problems on acyclic orientations of graphs, shellability of simplicial complexes, and acyclic partitions (Masahiro Hachimori).- Chapter 4. On ideal minimally non-packing clutters (Kenji Kashiwabara).- Chapter 5. Symmetric Travelling Salesman Problem (Tiru Arthanari).- Chapter 6. About the links between equilibrium problems and variational inequalities (D. Aussel).- Chapter 7. The shrinking projection method and resolvents on Hadamard spaces (Yasunori Kimura).- Chapter 8. Some Hard Stable Marriage Problems: A Survey on Multivariate Analysis (Sushmita Gupta).- Chapter 9. Approximate Quasi-Linearity for Large Incomes (Mamoru Kaneko).- Chapter 10. Cooperative Games in Networks under Uncertainty on the Costs (L. Mallozzi).- Chapter 11. Pricing competition between cell phone carriers in a growing market of customers (Andrey Garnaev).- Chapter 12. Stochastic games with endogenous transitions (Reinoud Joosten).

9 citations

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TL;DR: It is demonstrated how the concept of principal pivot transform can be effectively used to extend many existing results and revisit various results obtained for hidden Z class by Mangasarian, Cottle and Pang in context of solving linear complementarity problems as linear programs.

Abstract: In this paper, we explore various matrix-theoretic aspects of the hidden Z class and demonstrate how the concept of principal pivot transform can be effectively used to extend many existing results. In fact, we revisit various results obtained for hidden Z class by Mangasarian, Cottle and Pang in context of solving linear complementarity problems as linear programs. We identify hidden Z -matrices of special category and discuss the number of solutions of the associated linear complementarity problems. We also present game theoretic interpretation of various results related to hidden Z class and obtain proofs following the game theoretic approach of Raghavan for a subclass of Z -matrices.

4 citations

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TL;DR: A discrete variant of Farkas Lemma in the setting of a module over a linearly ordered commutative ring is reported, which may contain zero divisors and need not be associative nor unital.

Abstract: We report a discrete variant of Farkas Lemma in the setting of a module over a linearly ordered commutative ring. The ring may contain zero divisors, and need not be associative nor unital, but we need a certain hypothesis about the ring. Finally, we discuss the result and compare it with other related results found in the literature.

3 citations

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TL;DR: This paper considers the question of solving the quadratic programming problem of finding maximum of x T R x subject to x being a nonnegative vector with sum 1 and shows that for the class of simple graphs with resistance distance matrix ( R ) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratics programming problem.

Abstract: Quadratic programming problems involving distance matrix (D) that arises in trees are considered in the literature by Dankelmann (Discrete Math 312:12–20, 2012), Bapat and Neogy (Ann Oper Res 243:365–373, 2016). In this paper, we consider the question of solving the quadratic programming problem of finding maximum of $$x^{T}Rx$$ subject to x being a nonnegative vector with sum 1 and show that for the class of simple graphs with resistance distance matrix (R) which are not necessarily a tree, this problem can be reformulated as a strictly convex quadratic programming problem. An application to symmetric bimatrix game is also presented.

2 citations

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TL;DR: This paper revisits a result by Jurg et al. (Linear Algebra Appl 141:61–74, 1990) where the necessary and sufficient condition for a bimatrix game to be weakly completely mixed and presents an alternate proof of this result using linear complementarity approach.

Abstract: In this paper, we revisit a result by Jurg et al. (Linear Algebra Appl 141:61–74, 1990) where the necessary and sufficient condition for a bimatrix game to be weakly completely mixed is given. We present an alternate proof of this result using linear complementarity approach. We extend this result to a generalization of bimatrix game introduced by Gowda and Sznajder (Int J Game Theory 25:1–12, 1996) via a generalization of linear complementarity problem introduced by Cottle and Dantzig (J Comb Theory 8:79–90, 1970). We further study completely mixed switching controller stochastic game (in which transition structure is a natural generalization of the single controller games) and extend the results obtained by Filar (Proc Am Math Soc 95:585–594, 1985) for completely mixed single controller stochastic game to completely mixed switching controller stochastic game. A numerical method is proposed to compute a completely mixed strategy for a switching controller stochastic game.

2 citations

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01 Jan 2020

TL;DR: An iterative Q-method for solving a stochastic game based on the numerical identification of a characteristic function of a dynamic system in space of state-action is described and results of computer implementation of game Q- method are analyzed.

Abstract: The problem of incentive training of multi-agent systems in the game formulation for collective decision making under uncertainty is considered. Methods of incentive training do not require a mathematical model of the environment and enable decision making directly in the training process. Markov model of stochastic game is constructed and the criteria for its solution are formulated. An iterative Q-method for solving a stochastic game based on the numerical identification of a characteristic function of a dynamic system in space of state-action is described. Players’ current gains are determined by the method of randomization of payment Q-matrix elements. Mixed player strategies are calculated using the Boltzmann method. Pure strategies are determined on the basis of discrete random distributions given by mixed player strategies. The algorithm for stochastic game solving is developed and results of computer implementation of game Q-method are analyzed.

13 citations

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TL;DR: The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods as mentioned in this paper, and this can be circumvented by concentrating on the cons.

Abstract: The existence of a linear order on a group that is compatible with the group structure generally requires transfinite methods. However, this can be circumvented by concentrating on the cons...

9 citations

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25 May 2020TL;DR: Dynamic coordination of multi-agent systems (MAS) strategies under uncertainty based on a stochastic game model is solved and the method belongs to the class of reactive methods and simulates the reflexive behavior of living organisms.

Abstract: Dynamic coordination of multi-agent systems (MAS) strategies under uncertainty based on a stochastic game model is solved. Dynamic coordination is teaching of the system of generating spatially distributed periodic signals. A stochastic game model is built, criteria for dynamic coordination of player strategies are determined, a recurrent method, algorithmic and software for stochastic game solving are developed. The developed model, method and algorithm for stochastic game resolution provide dynamic MAS coordination, which is manifested in locally deter-mined spatial and temporal alignment of players’ strategies. Dynamic coordination is ensured by an adaptive search method for resolving stochastic play, taking into account current penalties for relevant spatial coordination and rhythm disturbances. It is established that the effectiveness of training players to perform coordinated rhythmic actions is determined by the balance between these penalties, which is achieved by the influence of white noise. Dynamic coordination of agent strategies is achieved as the real-time stochastic game is unleashed based on gathering current information and its adaptive processing. The considered method belongs to the class of reactive methods and simulates the reflexive behavior of living organisms. The method allows finding stochastic game solutions in pure strategies.

6 citations

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30 Dec 2019

TL;DR: This approach helps to avoid is coping all data if the content of a file has changed in separately, and is based on hash ring that is absorbing every incoming byte if the current hash mask or equal to a certain reach 64KB, there is division committed.

Abstract: The system for backing up the data is designed. Client software works on the computer of user, takes all the necessary files for backup, and turns them into Stream of bytes. Then breaks it into blocks (from 32 KB to 64KB) using a Rabin algorithm. It is based on hash ring that is absorbing every incoming byte if the current hash mask or equal to a certain reach 64KB, there is division committed. This approach helps to avoid is coping all data if the content of a file has changed in separately. For each data block client software calculates the

6 citations