A note on imposing strong complementary slackness conditions in DEA

Measurement of returns to scale using non-radial DEA models

There are some specific features of the non-radial DEA (data envelopment analysis) models which cause some problems under the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions in the optimization theor...

On the Strictly Complementary Slackness Relation in Linear Programming

Balinski and Tucker introduced in 1969 a special form of optimal tableaus for LP, which can be used to construct primal and dual optimal solutions such that the complementary slackness relation holds strictly. In this paper, first we note that using a polynomial time algorithm for LP Balinski and Tucker’s tableaus are obtainable in polynomial time. Furthermore, we show that, given a pair of pri...

Ranking of DMUs on interval data by imposing a minimum weight restriction in DEA

Lecture notes 5: Duality in applications

We have already seen how to take the dual of a linear program in general form. However, when we are solving a problem using linear programming, it can be very enlightening to take the dual of the linear program for that particular problem. Typically, in the context of the problem under study, it is possible to give a natural interpretation to the dual variables, and this also often leads to nat...

An Introduction to Duality in Convex Optimization

ABSTRACT This paper provides a short introduction to the Lagrangian duality in convex optimization. At first the topic is motivated by outlining the importance of convex optimization. After that mathematical optimization classes such as convex, linear and non-convex optimization, are defined. Later the Lagrangian duality is introduced. Weak and strong duality are explained and optimality condit...