In May 2008, the 48th workshop on ‘Nonsmooth Analysis, Optimization and Applications’ was organized by the International School of Mathematics ‘G. Stampacchia’ at the Ettore Majorana Centre for Scientific Culture in Erice, Sicily.
The conference was dedicated to Professor Vladimir F. Demyanov, on the occasion of his 70th birthday and in recognition of the role he had been playing for very long time both in foundation and in dissemination of nonsmooth analysis and related optimization techniques.
The development of nonsmooth analysis has been partly motivated by the need for solving, in fairly diverse advanced application fields, mathematical problems where differentiability of the involved functions is not guaranteed.
The design of effective algorithms for solving a wide range of optimization problems greatly benefited from the theoretical findings of Nonsmooth Analysis.
Starting from the pioneering works in the mid-1960s, Nonsmooth Analysis has, in particular, offered a valid support to applied areas such as decomposition techniques for large-scale mathematical programming problems, integer extremum problems tackled by means of the Lagrangian relaxation approach, numerical solution of variational inequalities, extremum problems with equilibrium constraints, classification and approximation problems, structural design, nonsmooth mechanics, etc.
People working on both sides of Nonsmooth Analysis and Optimization and Applications took part in the workshop, giving a number of significant contributions, some in terms of presentation of new results, some others in terms of state-of-the-art reviews and discussions of future perspectives.
After the workshop, we realized that such contributions did deserve a wider audience, and we asked Professor Oleg Burdakov to publish a special issue of the journal Optimization Methods and Software based on the talks presented in Erice. Our proposal was enthusiastically accepted, together with the decision of dedicating the special issue to Professor Vladimir F. Demyanov.
Early papers by Vladimir Fedorovich did appear in the 1960s and were focused on both theoretical and numerical treatment of (discrete or continuous) minmax problems. The fruitful co-operation with Vasily N. Malozemov did materialize in the classical book Introduction to Minimax, whose original Russian edition appeared in 1972.
In more recent years, he was studying the properties of a class of functions (the quasidifferentiable ones) whose directional derivatives can be expressed as the sum of a minimum and a maximum of a linear form over two convex and compact sets. In co-operation with Alexander M. Rubinov, the quasidifferential calculus was settled. A successive generalization led to the definition of the codifferentiable functions and of the related codifferential.
Vladimir Fedorovich's work has influenced many scientists. In addition, his unfailing enthusiasm was infectious to many people who, after him, entered the Nonsmooth Optimization field.
His personal characteristics such as sincerity, humour and intellectual curiosity have allowed him to remain a very active and stimulating person, particularly for young scientists.
For all these reasons, we proudly dedicate this work to Vladimir Fedorovich, wishing him good health and the same energy as ever.
We wish to express our deep gratitude to all contributors (the special issue contains 13 papers, by 25 mathematicians) for their fine works, to the referees for their careful and prompt reviews and to the Editor-in-Chief Oleg Burdakov for his friendly and valid support and guidance.