https://bura.brunel.ac.uk/bitstream/2438/17829/4/FullText.pdf

Big data analytics in supply chain management: A state-of-the-art literature review

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.

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Convex piecewise-linear fitting

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.

Generalized invexity and generalized invariant monotonicity

On Properties of Preinvex Functions

Some quantum integral inequalities via preinvex functions

We consider the polystochastic game in which the transition probabilities depend on the actions of a single player and the criterion is the limiting average of the expected costs for each player. Using linear complementarity theory, we present a computational scheme for computing a set of stationary equilibrium strategies and the corresponding costs for this game with the additional assumption that under any choice of stationary strategies for the players the resulting one step transition probability matrix is irreducible. This work extends our previous work on the computation of a set of stationary equilibrium strategies and the corresponding costs for a polystochastic game in which the transition probabilities depend on the actions of a single player and the criterion is the total discounted expected cost for each player.

Linear Complementarity and the Irreducible Polystochastic Game with the Average Cost Criterion When One Player Controls Transitions

In this chapter, we present some classes of generalized monotone maps and their relationship with the corresponding concepts of generalized convexity. We present results of generalized monotone maps that are used in the analysis and solution of variational inequality and complementarity problems. In addition, we obtain various characterizations and establish a connection between affine pseudomonotone mapping, affine quasimonotone mapping, positive-subdefinite matrices, generalized positive-subdefinite matrices, and the linear complementarity problem. These characterizations are useful for extending the applicability of Lemke’s algorithm for solving the linear complementarity problem.

Generalized Monotone Maps and Complementarity Problems

In this paper, we introduce a generalization of the polymatrix game (a nonzero sum noncooperativen-person game) considered by Howson and relate the problem of computing an equilibrium set of strategies for such a game to the generalized linear complementarity problem of Cottle and Dantzig. For an even more general version of the game we prove the existence of ane-equilibrium set of strategies. We also present a result on the stability of the equilibria based on degree theory.

Generalized linear complementarity in a problem ofn-person games

Let $T$ be a tree and let $D$ be the distance matrix of the tree. The problem of finding the maximum of $x'Dx$ subject to $x$ being a nonnegative vector with sum one occurs in many different contexts. These include some classical work on the transfinite diameter of a finite metric space, equilibrium points of symmetric bimatrix games and maximizing weighted average distance in graphs. We show that the problem can be converted into a strictly convex quadratic programming problem and hence it can be solved in polynomial time.

On a quadratic programming problem involving distances in trees

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.

S. K. Neogy

Papers

Linear Complementarity and the Irreducible Polystochastic Game with the Average Cost Criterion When One Player Controls Transitions

Generalized Monotone Maps and Complementarity Problems

Generalized linear complementarity in a problem ofn-person games

On a quadratic programming problem involving distances in trees

On solving a non-convex quadratic programming problem involving resistance distances in graphs