The logic relationship among the equality and inequality constraints in a standard constrained optimization problem (SCOP) is the logical AND. Various efficient, convergent and robust algorithms have been developed for such a SCOP. However, a more general constrained optimization problem (GCOP) with not only logic AND but also OR relationships exists in many practical applications. In order to solve such a generalized problem, a new mathematical transformations which can transfer a set of inequalities with logic OR into inequalities with logic AND relationships is developed. This transformation provides a necessary and sufficient condition which enables us to formulate real-time system design as a mixed Boolean-integer programming problem. A Branch and Bound Algorithm is applied to find the optimal solution. Experimental results have been presented to show its merits.