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Gopfert, A., Riahi, H., Tammer, Ch. and Zalinescu, C. (2003) Variational Methods in Partially Ordered Spaces. Springer, New York.

has been cited by the following article:

• TITLE: A New Global Scalarization Method for Multiobjective Optimization with an Arbitrary Ordering Cone

  AUTHORS: El-Desouky Rahmo, Marcin Studniarski

  KEYWORDS: Multiobjective Optimization, Scalarization Function, Generalized Jacobian, Vector Critical Point

  JOURNAL NAME: Applied Mathematics, Vol.8 No.2, February 24, 2017

  ABSTRACT: We propose a new scalarization method which consists in constructing, for a given multiobjective optimization problem, a single scalarization function, whose global minimum points are exactly vector critical points of the original problem. This equivalence holds globally and enables one to use global optimization algorithms (for example, classical genetic algorithms with “roulette wheel” selection) to produce multiple solutions of the multiobjective problem. In this article we prove the mentioned equivalence and show that, if the ordering cone is polyhedral and the function being optimized is piecewise differentiable, then computing the values of a scalarization function reduces to solving a quadratic programming problem. We also present some preliminary numerical results pertaining to this new method.