This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.
It is difficult to imagine modem technology without small particles, 1-1000 nm in size, because virtually every industry depends in some way on the use of such materials. Catalysts, printing inks, paper, dyes and pigments, many medicinal products, adsorbents, thickening agents, some adhesives, clays, and hundreds of other diverse products are based on or involve small particles in a very fundamental way. In some cases finely divided materials occur naturally or are merely a convenient form for using a material. In most cases small particles play a special role in technology because in effect they constitute a different state of matter because of the basic fact that the surface of a material is different from the interior by virtue of the unsaturated bonding interactions of the outermost layers of atoms at the surface of a solid. Whereas in a macroscale particle these differences are often insignificant, as the 9 surface area per unit mass becomes larger by a factor of as much as 10 , physical and chemical effects such as adsorption become so pronounced as to make the finely divided form of the bulk material into essentially a different material- usually one that has no macroscale counterpart.
It was in the middle of the 1980s, when the seminal paper by KarÂ markar opened a new epoch in nonlinear optimization. The importance of this paper, containing a new polynomial-time algorithm for linear opÂ timization problems, was not only in its complexity bound. At that time, the most surprising feature of this algorithm was that the theoretical preÂ diction of its high efficiency was supported by excellent computational results. This unusual fact dramatically changed the style and direcÂ tions of the research in nonlinear optimization. Thereafter it became more and more common that the new methods were provided with a complexity analysis, which was considered a better justification of their efficiency than computational experiments. In a new rapidly developÂ ing field, which got the name "polynomial-time interior-point methods", such a justification was obligatory. Afteralmost fifteen years of intensive research, the main results of this development started to appear in monographs [12, 14, 16, 17, 18, 19]. Approximately at that time the author was asked to prepare a new course on nonlinear optimization for graduate students. The idea was to create a course which would reflect the new developments in the field. Actually, this was a major challenge. At the time only the theory of interior-point methods for linear optimization was polished enough to be explained to students. The general theory of self-concordant functions had appeared in print only once in the form of research monograph .
Article Directory Articles
Article Directory Books