Geodesic
On localizing global Pareto solutions in a given convex set
Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 383-394
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Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing with respect to the cone generating the preference relation.
DOI : 10.4064/am-26-4-383-394
Keywords: sufficient and necessary conditions for optimality, Pareto optimal solutions, dual cones, feasible directions 
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Agnieszka Drwalewska; Lesław Gajek. On localizing global Pareto solutions in a given convex set. Applicationes Mathematicae, Tome 26 (1999) no. 4, pp. 383-394. doi: 10.4064/am-26-4-383-394

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