## Topics in Optimization |

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5-subarc adjoint admissible control assume assumption belongs Boosting Devices boundary conditions calculus of variations comp cone conic neighborhood consider const constant constraints continuous function control function control variable convex sets corner condition Corollary corresponding curve defined definition denotes derivatives determined differential equations discontinuity equations of motion Euclidean space Euler equations exists extremaloid families of extremals finite follows G. A. Bliss given grad gradient Hence implies inequality initial condition interior point interval Lagrange multipliers Lemma limiting surface linear locus matrix maximum principle minimizing necessary condition neighborhood nonzero obtain open ball optimal control optimal trajectory optimum problems parameter piecewise continuous Pontryagin's maximum principle positive number proof properties real numbers refraction region relation result satisfied scalar separating hyperplane singular arcs singular subarc solution space subset tangent term terminal Theorem thrust vanishes vector valued function Weierstrass criterion zero