Abstract
Vector optimization (polioptimization) problems are considered, where the solutions, constraints and performance are elements of linear topological spaces and a partial pre-ordering in performance space is implied by a positive cone. Ge¬neral scalarizing functionals are inve¬stigated which define a complete pre-ordering in performance space. Properties and disadvantages of Lagrange scalarizing functionals (Pareto method) are reviewed. Utopia point and reference point norm scalarization are discussed. A class of penalty scalarization methods is defined. Fundamental properties of penalty scalarizing functionals are presented. Penalty polioptimization algorithms are formulated and their effectiveness is shown by computational examples related to control theory and practice.
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