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Set Optimization and Applications : The State of the Art: from Set Relations to Set-valued Risk Measures
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‘Set Optimization’ is a theory for minimization/maximization problems with a set-valued objective. While conventional approaches focus on minimal/maximal elements with respect to vector orders or set relations, the new ‘complete-lattice approach’ comprises for the first time a coherent solution concept for set optimization problems, along with existence results, duality theorems, optimality conditions and the theoretical foundations of numerical algorithms. The theory has already found striking applications in Mathematical Finance, where it allows fundamental results for market models with transaction costs to be obtained using set optimization methods. There is no comparable volume on the market, making the book an invaluable resource for researchers working in Vector Optimization and Multi-Criteria Decision Making, Set Optimization, Mathematical Finance and (Set-Valued) Variational Analysis.