Single-ratio and multi-ratio fractional programs in applications are often generalized convex programs. We begin with a survey of applications of single-ratio fractional programs, min-max fractional programs and sum-of-ratios fractional programs. Given the limited advances for the latter class...

We present a thorough analysis of the economic order quantity model with shortages under a general inventory cost rate function and concave production costs. By using some standard results from convex analysis, we show that the model exhibits a composite concave-convex structure. Consequently,...

In this paper which will appear as a chapter in the Handbook of Generalized Convexity we discuss the basic ideas of convex and quasiconvex analysis in finite dimensional Euclidean spaces. To illustrate the usefulness of this branch of mathematics also applications to optimization theory and...

Airline revenue management is the practice of controlling the booking requests such that the planes are filled with the most profitable passengers. In revenue management the capacities of the business and economy class sections of the plane are traditionally considered to be fixed and distinct...

The present paper proposes a new approach to solve generalized fractional programming problems through user interaction. Capitalizing on two alternatives, we review the Dinkelbach-type methods and set forth the main difficulty in applying these methods. In order to cope with this difficulty, we...

In this paper we discuss the level set method of Joó and how to use it to give an elementary proof of the well-known Sion’s minimax result. Although this proof technique is initiated by Joó and based on the inter-section of upper level sets and a clever use of the topological notion of...

An alternative smoothing method for the high dimensional max function has been studied. The proposed method is a recursive extension of the two dimensional smoothing functions. In order to analyze the proposed method, a theoretical framework related to smoothing methods has been discussed....

The present paper discusses an approach to solve the joint replenishment problem in a production environment with concave production cost functions. Under this environment, the model leads to a global optimization problem, which is investigated by using some standard results from convex...

We consider equilibrium constrained optimization problems, which have a general formulationthat encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated K K M lemma, we...

Direct marketing firms want to transfer their message as efficiently as possible in order to obtain a profitable long-term relationship with individual customers. Much attention has been paid to address selection of existing customers and on identifying new profitable prospects. Less attention...