Vector optimization

Vector optimization is a subarea of mathematical optimization where optimization problems with vector-valued objective functions are optimized with respect to a given partial ordering and subject to certain constraints. A multi-objective optimization problem is a special case of a vector optimization problem: The objective space is the finite dimensional Euclidean space partially ordered by the component-wise "less than or equal to" ordering.

f:X→Z for a partially ordered vector space X is an arbitrary set and x∈S one has x∈S one has x¯ is a weakly efficient point with respect to a closed pointed convex cone ℝ+d is the non-negative orthant of Andreas Löhne (2011). Vector Optimization with Infimum and Supremum. Springer. ISBN 9783642183508.