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Quasiconvex Programming and its Applications: Quasiconvex Maximization Problem Quasiconvex Minimization Problem Nonconvex Optimal control Problem Applications - Couverture souple

Rentsen, Enkhbat

 
9783838308074: Quasiconvex Programming and its Applications: Quasiconvex Maximization Problem Quasiconvex Minimization Problem Nonconvex Optimal control Problem Applications
Couverture souple
ISBN 10 : 3838308077 ISBN 13 : 9783838308074
Editeur : LAP Lambert Academic Publishing, 2009

Synopsis

Notion of convexity plays an important role in Economics and Engineering. The general equilibrium theory is based on convex programming. In classical economics, production and utility functions are assumed to be concave functions and as consequence, demand and cost functions are convex. The firm theory requires to solve the concave maximization problem while consumer theory considers utility maxmization problem. In recent years, generalized convex functions such as quasiconvex functions are found to be useful in Economics. In this book we consider two problems of maximizing and minimizing a quasiconvex function. Both problems belong to a class of global optimization and application of classical conditions has not been successful for solving these problems. Moreover, the Lagrangean method provides only a stationary point without guarantee of local optimality. For these reasons, global optimization appears to require new methods different from the standard nonlinear programming techniques. We derive new global optimality conditions for our problems and construct some algorithms the for convex case. We show applications of quasiconvex programming in economics and engineering.

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Présentation de l'éditeur

Notion of convexity plays an important role in Economics and Engineering. The general equilibrium theory is based on convex programming. In classical economics, production and utility functions are assumed to be concave functions and as consequence, demand and cost functions are convex. The firm theory requires to solve the concave maximization problem while consumer theory considers utility maxmization problem. In recent years, generalized convex functions such as quasiconvex functions are found to be useful in Economics. In this book we consider two problems of maximizing and minimizing a quasiconvex function. Both problems belong to a class of global optimization and application of classical conditions has not been successful for solving these problems. Moreover, the Lagrangean method provides only a stationary point without guarantee of local optimality. For these reasons, global optimization appears to require new methods different from the standard nonlinear programming techniques. We derive new global optimality conditions for our problems and construct some algorithms the for convex case. We show applications of quasiconvex programming in economics and engineering.

Biographie de l'auteur

Rentsen Enkhbat is a Professor of the National University of Mongolia. He received his Ph.D degree from Irkutsk State University in Applied Mathematics. He has held visiting appointments at the University of Massachusetts, Kyoto University, Ibaraki University, Humbold University Berlin, University of Florida, KAIST(Korea).

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
LAP Lambert Academic Publishing
Date d'édition
2009
Langue
anglais
ISBN 10 
3838308077
ISBN 13 
9783838308074
Reliure
Broché
Nombre de pages
160
Coordonnées du fabricant
non disponible
Personne responsable
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