On Optimality Conditions for Multi-objective Problems with a Euclidean Cone of Preferences

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.