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.

/pdf/convex-piecewise-linear-fitting-49d8ptyg8q.pdf

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

In this paper we consider a common optimization problem faced by a printing company while designing masters for advertisement material. A printing company may receive from various customers, advertisements for their products and services and their demand is for a specified number of copies to be printed. In a particular case, the printer receives these orders to be delivered next week from the customers, until the Thursday of a week. By Monday the printed copies have to be delivered to the customers. These advertisement items of the various customers are to be printed on large sheets of papers of specified standard sizes. The size is called a k-up if k items can be printed on one sheet. It is a given constraint that only items of the same size can be loaded on a master. This constraint results in a decomposition of the original problem of designing masters into many sub-problems, one for each size. The objective is to minimize the number of masters required while meeting the requirements of the customers. We formulate this optimization problem mathematically, discuss the computational issues and present some heuristic approaches for solving the problem.

An Optimization Model to Determine Master Designs and Runs for Advertisement Printing

Modeling a Jamming Game for Wireless Networks (A Garnaev) Existence of Nash Networks in the One-Way Flow Model of Network Formation (J Derks et al.) Strategic Advertisement with Externalities: A New Dynamic Approach (R Joosten) A New Axiomatization of the Shapley Value for TU-Games in Terms of Semi-Null Players Applied to 1-Concave Games (T S H Driessen) Coextrema Additive Operators (T Ui et al.) Models without Main Players (T S Arthanari) Weak Convergence of an Iterative Scheme with a Weaker Coefficient Condition (Y Kimura) Complementarity Modeling and Game Theory: A Survey (S K Neogy & A K Das) and other papers.

Modeling, computation and optimization

In this article, we revisit the applications of principal pivot transform and its generalization for a rectangular matrix (in the context of vertical linear complementarity problem) to solve some structured classes of zero-sum two-person discounted semi-Markov games with finitely many states and actions. The single controller semi-Markov games have been formulated as a linear complementarity problem and solved using a stepwise principal pivoting algorithm. We provide a sufficient condition for such games to be completely mixed. The concept of switching controller semi-Markov games is introduced and we prove the ordered field property and the existence of stationary optimal strategies for such games. Moreover, such games are formulated as a vertical linear complementarity problem and have been solved using a stepwise generalized principal pivoting algorithm. Sufficient conditions are also given for such games to be completely mixed. For both these classes of games, some properties analogous to completely mixed matrix games, are established.

S. K. Neogy

Papers

An Optimization Model to Determine Master Designs and Runs for Advertisement Printing

Modeling, computation and optimization

Completely Mixed Strategies for Two Structured Classes of Semi-Markov Games, Principal Pivot Transform and Its Generalizations

Operations research with economic and industrial applications: emerging trends

On hidden Z-matrices and the linear complementarity problem