Necessary and sufficient conditions for optimality in linear-quadratic problems of optimal control

Linear-quadratic Bolza problems of optimal control with variable end points are considered. Under the strengthened Legendre condition, necessary and sufficient optimality conditions are established, and it is shown that the linear-quadratic Bolza problem of optimal control can be reduced to a quadratic minimization problem in a finite-dimensional space. Simple simulations where solutions of a nonlinear problem can be recovered from solutions of the accessory linear-quadratic problem are indicated. Conjectures regarding sufficient conditions for optimality in nonlinear Bolza problems are included