Mitiku, Semu (PhD)Chalchisa, Mengistu2018-07-172023-11-042018-07-172023-11-042013-07-02http://etd.aau.edu.et/handle/123456789/8837This paper gives a review for optimal control problems with state variable inequality constraints. To solve the problem with pure state inequality constraint, we use different approaches such that: direct adjoint approach, the indirect adjoining approach with complementary slackness (first order constraints), the indirect adjoining approach for higher order constraints and the indirect adjoining approach with continuous adjoint functions. Furthermore, the application of optimal control problems conditions is demonstrated by solving illustrative examples. Keywords: Optimal control problems, pure state inequality constraint and mixed state inequality constraintenOptimal control problemspure state inequality constraint and mixed state inequality constraintThesis