The contributions in this volume aim to deepenunderstanding of some of the current research problems and theories inmodern topics such as calculus of variations, optimization theory, complexanalysis, real analysis, differential equations, andgeometry. Applications to these areas of mathematics are presented withinthe broad spectrum of research in Engineering Science withparticular emphasis on equilibrium problems, complexity in numericaloptimization, dynamical systems, non-smooth optimization, complex networkanalysis, statistical models and data mining, and energy systems. Additionalemphasis is given to interdisciplinary research, although subjects are treatedin a unified and self-contained manner. The presentation of methods, theory andapplications makes this tribute an invaluable reference for teachers,researchers, and other professionals interested in pure and appliedresearch, philosophy of mathematics, and mathematics education. Somereview papers published in this volume will be particularly useful for abroader audience of readers as well as for graduate students who search for thelatest information.    ?ConstantinCarathéodory’s wide-ranging influence in the international mathematicalcommunity was seen during the first Fields Medals awards at the InternationalCongress of Mathematicians, Oslo, 1936. Two medals were awarded, one to Lars V. Ahlfors and one to Jesse Douglass. It was Carathéodory who presented both theirworks during the opening of the International Congress. This volume containssignificant papers in Science and Engineering dedicated to the memory ofConstantin Carathéodory and the spirit of his mathematical influence.