Semiparametric proper efficiency principles and duality models for constrained multiobjective fractional optimal control problems containing arbitrary norms

Abstract

Semiparametric necessary and sufficient proper efficiency conditions are established for a class of constrained multiobjective fractional optimal control problems with linear dynamics, containing arbitrary norms. Moreover, utilizing these proper efficiency results, eight semiparametric duality models are formulated and appropriate duality theorems are proved. These proper efficiency and duality criteria contain, as special cases, similar results for several classes of unorthodox optimal control problems with multiple, fractional, and conventional objective functions, which are particular cases of the main problem considered in this paper.