GENERALIZED CONVEXITY,
GENERALIZED MONOTONICITY
AND APPLICATIONS
Nonconvex Optimization and Its Applications
Volume 77
Managing Editor:
Panos Pardalos
University of Florida, U.S.A.
Advisory Board:
J. R. Birge
University of Michigan, U.S.A.
Ding-Zhu Du
University of Minnesota, U.S.A.
C. A. Floudas
Princeton University, U.S.A.
J. Mockus
Lithuanian Academy of Sciences, Lithuania
H. D. Sherali
Virginia Polytechnic Institute and State University, U.S.A.
G. Stavroulakis
Technical University Braunschweig, Germany
H.Tuy
National Centre for Natural Science and Technology, Vietnam
GENERALIZED CONVEXITY,
GENERALIZED MONOTONICITY
AND APPLICATIONS
Proceedings of the International
Symposium on Generalized Convexity
and Generalized Monotonicity
Edited by
ANDREW EBERHARD
RMIT University, Australia
NICOLAS HADJISAVVAS
University of the Aegean, Greece
DINH THE LUC
University of Avignon, France
Springer
eBook ISBN: 0-387-23639-2
Print ISBN:
0
-387-23638-4
Print ©2005 Springer Science + Business Media, Inc.
All rights reserved
No part of this eBook may be reproduced or transmitted in any form or by any means, electronic,
mechanical, recording, or otherwise, without written consent from the Publisher
Created in the United States of America
Boston
©2005 Springer Science + Business Media, Inc.
Visit Springer's eBookstore at: http://ebooks.kluweronline.com
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Contents
Preface
Part I
INVITED PAPERS
1
Algebraic Dynamics of Certain Gamma Function Values
J.M. Borwein and K. Karamanos
2
(Generalized) Convexity and Discrete Optimization
Rainer E. Burkard
3
Lipschitzian Stability of Parametric Constraint Systems in Infinite
Dimensions
Boris S. Mordukhovich
4
Monotonicity in the Framework of Generalized Convexity
Hoang Tuy
Part II CONTRIBUTED PAPERS
5
On the Contraction and Nonexpansiveness Properties of the Margi-
nal Mappings in Generalized Variational Inequalities Involving
co-Coercive Operators
Pham Ngoc Anh, Le Dung Muu, Van Hien Nguyen and Jean-Jacques Strodiot
6
A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian
Multivalued Variational Inequalities
T. Q. Bao and P. Q. Khanh
7
Duality in Multiobjective Optimization Problems with Set Constraints
Riccardo Cambini and Laura Carosi
ix
3
23
39
61
89
113
131
vi
GENERALIZED CONVEXITY AND MONOTONICITY
8
Duality in Fractional Programming Problems with Set Constraints
Riccardo Cambini, Laura Carosi and Siegfried Schaible
9
On the Pseudoconvexity of the Sum of two Linear Fractional Functions
Alberto Cambini, Laura Martein and Siegfried Schaible
10
Bonnesen-type Inequalities and Applications
A.
Raouf Chouikha
11
Characterizing Invex and Related Properties
B.
D. Craven
12
Minty Variational Inequality and Optimization: Scalar and Vector
Case
Giovanni P. Crespi, Angelo Guerraggio and Matteo Rocca
13
Second Order Optimality Conditions for Nonsmooth Multiobjective
Optimization Problems
Giovanni
P. Crespi, Davide La Torre and Matteo Rocca
14
Second Order Subdifferentials Constructed using Integral Convolu-
tions Smoothing
Andrew
Eberhard, Michael Nyblom and Rajalingam Sivakumaran
15
Applying Global Optimization to a Problem in Short-Term Hy-
drothermal Scheduling
Albert Ferrer
16
for Nonsmooth Programming on a Hilbert Space
Misha G. Govil and Aparna Mehra
17
Identification of Hidden Convex Minimization Problems
Duan Li, Zhiyou Wu, Heung Wing Joseph Lee, Xinmin Yang and Liansheng
Zhang
18
On Vector Quasi-Saddle Points of Set-Valued Maps
Lai-Jiu Lin and Yu-Lin Tsai
19
New Generalized Invexity for Duality in Multiobjective Program-
ming Problems Involving N-Set Functions
147
161
173
183
193
213
229
263
287
299
311
321
Contents
S.K. Mishra, S.Y. Wang, K.K. Lai and J. Shi
20
Equilibrium Prices and Quasiconvex Duality
Phan Thien Thach
vii
341
Preface
In recent years there is a growing interest in generalized convex func-
tions and generalized monotone mappings among the researchers of ap-
plied mathematics and other sciences. This is due to the fact that
mathematical models with these functions are more suitable to describe
problems of the real world than models using conventional convex and
monotone functions. Generalized convexity and monotonicity are now
considered as an independent branch of applied mathematics with a wide
range of applications in mechanics, economics, engineering, finance and
many others.
The present volume contains 20 full length papers which reflect cur-
rent theoretical studies of generalized convexity and monotonicity, and
numerous applications in optimization, variational inequalities, equilib-
rium problems etc. All these papers were refereed and carefully selected
from invited talks and contributed talks that were presented at the 7th
International Symposium on Generalized Convexity/Monotonicity held
in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is orga-
nized by the Working Group on Generalized Convexity (WGGC) every
3 years and aims to promote and disseminate research on the field. The
WGGC (http://www.genconv.org) consists of more than 300 researchers
coming from 36
countries.
Taking this opportunity, we want to thank all speakers whose contri-
butions make up this volume, all referees whose cooperation helped in en-
suring the scientific quality of the papers, and all people from the Hanoi
Institute of Mathematics whose assistance was indispensable in running
the symposium. Our special thanks go to the Vietnam Academy of
Sciences and Technology, the Vietnam National Basic Research Project
“Selected problems of optimization and scientific computing” and the
Abdus Salam International Center for Theoretical Physics at Trieste,
Italy, for their generous support which made the meeting possible. Fi-
nally, we express our appreciation to Kluwer Academic Publishers for
including this volume into their series. We hope that the volume will
x
GENERALIZED CONVEXITY AND MONOTONICITY
be useful for students, researchers and those who are interested in this
emerging field of applied mathematics.
ANDREW EBERHARD
NICOLAS HADJISAVVAS
DINH THE LUC