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Optimality Conditions and Image Space Analysis for Vector Optimization Problems

  • Giandomenico Mastroeni
Chapter
Part of the Vector Optimization book series (VECTOROPT, volume 1)

Abstract

At the beginning of last century, W. Pareto introduced, in the field of Economics the idea of considering the simultaneous extremization of more that one objective function, namely a Vector Optimization Problem (VOP). This new concept has much influenced the Theory of Economics and the mathematical theory of extrema, but, in the first half of the century, only a few applications has been developed. After the second world war, in some fields of Engineering [53] and in the context of Industrial Systems, Logistics and Management Science, there has been an increasing request of mathematical models for optimizing situations with concurrent objectives, and nowadays, besides the above mentioned applications, VOP also arises in the field of statistics, approximation theory and cooperative game theory [18, 33].

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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PisaPisaItaly

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