Special Issue on Variational Analysis and Optimization

Abstract

This issue of SIAM Journal on Optimization was motivated by the September 2005 Workshop on Well-Posedness of Optimization Problems and Related Topics, held in Borovets, Bulgaria. This workshop was the tenth event of a series initiated in 1987 as a small meeting of Bulgarian and Italian mathematicians working on the subject. Since then, this series has gained a high international reputation, and its workshops are attractive scientific events where modern research of leading experts is presented and lively discussions stimulate and motivate young scientists. The workshops have substantially increased their scope by including stability, sensitivity, and well-posedness of problems in optimization, optimal control, and calculus of variations, variational principles, advances in stochastic optimization, vector optimization, set-valued analysis, and so on. We view variational analysis as a large area of modern mathematics encompassing not only ideas of the classical calculus of variations and optimization but also to a large extent perturbations and approximations, set-valued analysis, generalized differential calculus, and generalized convexity. Interaction with other branches of mathematics and with engineering and economics brought interesting and unexpected applications of variational analysis and nonsmooth optimization. Recent developments in mathematical finance, actuarial mathematics, and statistics have been major driving forces for the theory and numerical methods of optimization. This volume presents 23 papers authored or co-authored by the participants. The topics reflect the field's diversity and vitality. They highlight many interesting recent advances and indicate some problems that may become focus of future research. Many people have made this collection possible. We would like to express our gratitude to all organizations who supported the Borovets workshop and to the local organizers who created the productive and supportive atmosphere of the meeting. We are grateful to the authors for their contributions and to the referees for their excellent and timely work. Finally, we offer our thanks to the SIAM Vice-President for Publications, Tim Kelley; to the Editor-in-Chief of SIAM Journal on Optimization, Nick Gould; and SIAM staffers Mitch Chernoff and Brian Fauth, who have encouraged us to prepare this special issue and have supported us in the process of editing it. We hope that this collection of papers provides an interesting mathematical lecture and an inspiration for further research.