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.
Magnetic nanoparticles (NPs) are finding their place in many modern technologies such as electronics (memory or spintronic devices) and medicine (contrast media, electromagnetic thermal therapy) to name just a few examples. The application of modern techniques based on synchrotron radiation, in particular X-ray spectroscopies, as well as an rf transverse susceptibility probe, built ad hoc, allowed the author to investigate several classes of magnetic NPs with diverse applications. For example, the interesting anisotropic properties of CoW and CoPt NPs revealed new magnetic behaviour and phases. Gold NPs prepared on a biological template from Sulfolobus acidocaldarius S-layer, were shown to possess intrinsic magnetism caused by the electron exchange with the sulfur atoms of the template. Silica and oleic acid coated magnetite NPs showed excellent human compatibility while preserving the bulk magnetic figures of merit. Both macroscopic and microscopic properties of all these NPs, hitherto unexplained, have been revealed for the first time.
Arguably, many industrial optimization problems are of the multiobjective type. The present work, after providing a survey of the state of the art in multiobjective optimization, gives new insight into this important mathematical field by consequently taking up the viewpoint of differential geometry. This approach, unprecedented in the literature, very naturally results in a generalized homotopy method for multiobjective optimization which is theoretically well-founded and numerically efficient. The power of the new method is demonstrated by solving two real-life problems of industrial optimization.
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