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

Principal pivot transforms of some classes of matrices

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.

Pivoting algorithms for some classes of stochastic games: a survey

On a Mixture Class of Stochastic Game with Ordered Field Property

In this article, we present a weaker version of the class of generalized positive subdefinite matrices introduced by Crouzeix and Komlosi [J.P. Crouzeix and S. Komlosi, The Linear Complementarity Problem and the Class of Generalized Positive Subdefinite Matrices, Applied Optimization, Vol. 59, Kluwer, Dordrecht, 2001, pp. 45–63], which is new in the literature, and obtain some properties of weak generalized positive subdefinite (WGPSBD) matrices. We show that this weaker class of matrices is also captured by row-sufficient matrices introduced by Cottle et al. [R.W. Cottle, J.S. Pang, and V. Venkateswaran, Sufficient matrices and the linear complementarity problem, Linear Algebra Appl. 114/115 (1989), pp. 231–249] and show that for WGPSBD matrices under appropriate assumptions, 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. This further extends the results obtained in an earlier paper by...

On weak generalized positive subdefinite matrices and the linear complementarity problem

In this paper, we consider the generalized linear complementarity problem VLCP $(q,A)$ where $A$ is a vertical block $Z$-matrix. We prove that the Cottle--Dantzig pivoting algorithm can process this problem by showing that this algorithm generates the same sequence of bases that a modified simplex algorithm for minimizing the artificial variable $z_{0}$ does. We also show that a modified version of the Cottle--Dantzig algorithm can be used for determining whether a given vertical block $Z$-matrix is a vertical block $P_{0}$-matrix.

S. K. Neogy

Papers

Principal pivot transforms of some classes of matrices

Pivoting algorithms for some classes of stochastic games: a survey

On a Mixture Class of Stochastic Game with Ordered Field Property

On weak generalized positive subdefinite matrices and the linear complementarity problem

Algorithms For The Generalized Linear Complementarity Problem With A Vertical Block Z -Matrix