A parametric approach for solving a class of generalized quadratic-transformable rank-two nonconvex programs

AbstractThe aim of this paper is to propose a solution algorithm for a particular class of rank-two nonconvex programs having a polyhedral feasible region. The algorithm is based on the so-called “optimal level solutions” method. Various global optimality conditions are discussed and implemented in order to improve the efficiency of the algorithm

On the minimization of a class of generalized linear functions on a flow polytope

The aim of this paper is to propose a solution method for the minimization of a class of generalized linear functions on a flow polytope. The problems will be solved by means of a network algorithm, based on graph operations, which lies within the class of the so-called 'optimal level solutions' parametric methods. The use of the network structure of flow polytopes, allows to obtain good algorithm performances and small numerical errors. Results of a computational test are also provided

CONCAVITA' GENERALIZZATA: CASO SCALARE E CASO VETTORIALE

1993/1994VII Ciclo1968Versione digitalizzata della tesi di dottorato cartacea. Nell'originale cartaceo errata numerazione delle pagin

Generating the efficient frontier of a class of bicriteria generalized fractional programming

In this paper, a particular class of bicriteria maximization problems over a compact polyhedron is considered. The first component of the objective function is the ratio of powers of affine functions and the second one is linear. Several theoretical properties are provided, such as the pseudoconcavity of the first criterium of the objective function, the connectedness and compactness of both the efficient frontier and the set of efficient points. The obtained results allow us to propose a new simplex-like solution method for generating the whole efficient frontier; to better clarify the use of the suggested algorithm, several examples are described and the results of a computational test are presented

A reduced formulation for pseudoinvex vector functions

Vector pseudoinvexity is characterized in the current literature by means of a suitable functional which depends on two variables. In this paper, vector pseudoinvexity is characterized by means of a functional which depends on one variable only. For this very reason, the new characterizing conditions are easier to be verified

Simplex-like sequential methods for a class of generalized fractional programs

A sequential method for a class of generalized fractional programming problems is proposed. The considered objective function is the ratio of powers of affine functions and the feasible region is a polyhedron, not necessarily bounded. Theoretical properties of the optimization problem are first established and the maximal domains of pseudoconcavity are characterized. When the objective function is pseudoconcave in the feasible region, the proposed algorithm takes advantage of the nice optimization properties of pseudoconcave functions; the particular structure of the objective function allows to provide a simplex-like algorithm even when the objective function is not pseudoconcave. Computational results validate the nice performance of the proposed algorithm

Optimal pricing and promotional effort control policies for a new product growth in segmented market

Market segmentation enables the marketers to understand and serve the customers more effectively thereby improving company’s competitive position. In this paper, we study the impact of price and promotion efforts on evolution of sales intensity in segmented market to obtain the optimal price and promotion effort policies. Evolution of sales rate for each segment is developed under the assumption that marketer may choose both differentiated as well as mass market promotion effort to influence the uncaptured market potential. An optimal control model is formulated and a solution method using Maximum Principle has been discussed. The model is extended to incorporate budget constraint. Model applicability is illustrated by a numerical example. Since the discrete time data is available, the formulated model is discretized. For solving the discrete model, differential evolution algorithm is used

Generalized Concavity for Bicriteria Functions

In this paper some classes of vector valued generalized concave functions will be compared in the bicriteria case, that is when the images of the functions are contained in R-2. We will prove that, in the bicriteria case, continuous (C,C)-quasiconcave functions coincide with C-quasiconcave functions introduced by Luc; we will also prove that (C, C)-quasiconcave functions have a first order characterization and that they can be characterized by means of their increasness and decreasness

Composition Theorems for Generalized Concave Vector Valued Functions

The aim of this paper is to extend to the vector case some composition theorems and properties related to generalized concave scalar functions. The vector valued functions which will be used are defined by means of a partial order given by a closed convex cone with nonempty interior. Results about composition theorems concerning generalized concave scalar functions are also provided

Underestimation functions for a rank-two partitioning method

Low rank problems are nothing but nonlinear minimization problems over polyhedrons where a linear transformation of the variables provides an objective function which actually depends on very few variables. These problems are often used in in applications, for example in concave quadratic minimization problems, multiobjective/bicriteria programs, location-allocation models, quantitative management science, data envelopment analysis, efficiency analysis and performance measurement. The aim of this paper is to deepen on the study of a solution method for a class of rank-two nonconvex problems having a polyhedral feasible region expressed by means of inequality/box constraints and an objective function of the kind $phi(c^Tx+c_0,d^Tx+d_0)$. The rank-two structure of the problem allows to determine various localization conditions and underestimation functions. The stated theoretical conditions allow to determine a solution algorithm for the considered class of rank-two problems whose performance is witnessed by means of a deep computational test