@article{1484787,
      recid = {1484787},
      author = {Göpfert, A. and Riahi, Hassan, and Tammer, Christiane, and  Zalinescu, C.,},
      title = {Variational methods in partially ordered spaces /},
      pages = {1 online resource (550 pages) :},
      abstract = {In mathematical modeling of processes occurring in  logistics, management science, operations research,  networks, mathematical finance, medicine, and control  theory, one often encounters optimization problems  involving more than one objective function so that  Multiobjective Optimization (or Vector Optimization,  initiated by W. Pareto) has received new impetus. The  growing interest in vector optimization problems, both from  the theoretical point of view and as it concerns  applications to real world optimization problems, asks for  a general scheme which embraces several existing  developments and stimulates new ones. This book aims to  provide the newest results and applications of this quickly  growing field. Basic tools of partially ordered spaces are  discussed and applied to variational methods in nonlinear  analysis and to optimization problems. The book begins by  providing simple examples that illustrate what kind of  problems can be handled with the methods presented. The  book then deals with connections between order structures  and topological structures of sets, discusses properties of  nonlinear scalarization functions, and derives  corresponding separation theorems for not necessarily  convex sets. Furthermore, characterizations of set  relations via scalarization are presented. Important  topological properties of multifunctions and new results  concerning the theory of vector optimization and  equilibrium problems are presented in the book. These  results are applied to construct numerical algorithms,  especially, proximal-point algorithms and geometric  algorithms based on duality assertions. In the second  edition, new sections about set less relations, optimality  conditions in set optimization and the asymptotic behavior  of multiobjective Pareto-equilibrium problems have been  incorporated. Furthermore, a new chapter regarding scalar  optimization problems under uncertainty and robust  counterpart problems employing approaches based on vector  optimization, set optimization, and nonlinear scalarization  was added. Throughout the entire book, there are examples  used to illustrate the results and check the stated  conditions. This book will be of interest to graduate  students and researchers in pure and applied mathematics,  economics, and engineering. A sound knowledge of linear  algebra and introductory real analysis should provide  readers with sufficient background for this book. .},
      url = {http://library.usi.edu/record/1484787},
      doi = {https://doi.org/10.1007/978-3-031-36534-8},
}