- OPTIMALITY CONDITIONS AND DUALITY MODELS FOR MINMAX FRACTIONAL OPTIMAL CONTROL PROBLEMS CONTAINING ARBITRARY NORMS
- G. J., Zalmai ;
- Journal of the Korean Mathematical Society, volume 41, issue 5, 2004, Pages 821~864
- DOI : 10.4134/JKMS.2004.41.5.821

Abstract

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable 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 semi definite 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.