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Article

A Note on Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

Journal of Optimization Theory and Applications. 2015. Vol. 166. No. 3. P. 791-803.
A.Y. Golubin.

The paper suggests a new — to the best of the author’s knowledge—characterization of decisions, which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a prescribed angular radius. The main idea is to use the angle distances between the unit vector and points of utility space. A necessary and sufficient condition for the optimality in the form of an equation is derived. The first-order necessary optimality conditions are also obtained.