Journal of the
Korean Mathematical Society JKMS

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondifferentiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semidefinite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

Keywords: minmax fractional optimal control problems, constraints, arbitrary norms, optimality conditions, duality models, duality theorems

MSC numbers: Primary 49K35, 49N15; Secondary 90C32, 90C47