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Geometrical Optimality Conditions for Strongly and Lexicographically Optimal Solutions in Convex Multicriteria Programming

Marko M. Mäkelä, Yury Nikulin, Geometrical Optimality Conditions for Strongly and Lexicographically Optimal Solutions in Convex Multicriteria Programming. TUCS Technical Reports 920, Turku Centre for Computer Science, 2008.

Abstract:

Various type of optimal solutions of multiobjective optimization problems can be characterized by means of different cones. Provided the partial objectives are convex, we derive necessary and sufficient geometrical optimality conditions for strongly efficient and lexicographically optimal solutions by using tangent, contingent and normal cones. Combining new results with previously known ones, we derive two general schemes reflecting structural properties and interconnections of five optimality principles: weakly and properly Pareto optimality, efficiency and strongly efficiency as well as lexicographic optimality.

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BibTeX entry:

@TECHREPORT{tMaNi08a,
  title = {Geometrical Optimality Conditions for Strongly and Lexicographically Optimal Solutions in Convex Multicriteria Programming},
  author = {Mäkelä, Marko M. and Nikulin, Yury},
  number = {920},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2008},
}

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