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We consider an optimal control problem for systems governed by nonlinear ordinary differential equations, with control and state constraints, including pointwise state constraints. The problem is formulated in the classical and in the relaxed form. Various necessary/sufficient conditions for optimality are first given for both problems. For the numerical solution of these problems, we then propose a penalized gradient projection method generating classical controls, and a penalized conditionaldoi:10.12988/imf.2007.07135 fatcat:l2glo22subfdrodcfjpoyiijya