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CHAPTER 1 NECESSARY CONDITIONS FOR AN EXTREMUM
CHAPTER 2 NECESSARY CONDITIONS FOR AN EXTREMUM IN THE CLASSICAL PROBLEMS OF THE CALCULUS OF VARIATIONS AND...
CHAPTER 3 ELEMENTS OF CONVEX ANALYSIS
CHAPTER 4 LOCAL CONVEX ANALYSIS
CHAPTER 5 LOCALLY CONVEX PROBLEMS AND THE MAXIMUM PRINCIPLE FOR PROBLEMS WITH PHASE CONSTRAINTS
CHAPTER 6 SPECIAL PROBLEMS
CHAPTER 7 SUFFICIENT CONDITIONS FOR AN EXTREMUM
absolutely continuous assertion assume assumption Banach space boundary conditions bounded calculus of variations called Chapter classical calculus closed compact cone conjugate consider continuous linear continuously differentiable conv converges convex set Corollary deﬁned deﬁnition denote derivative domain epi f equality Euler equation exists a number extremal problems extremum f is continuous ﬁeld ﬁnd ﬁnite ﬁxed formula Frechet differentiable function f function x(t implies inﬁmum integral K-function Lagrange function Lagrange multipliers Lagrange problem Lagrangian Legendre Lemma Let f linear functional locally convex lower semicontinuous mapping F Math maximum principle minimum multimapping Nauk necessary conditions neighborhood non-empty non-negative obtain optimal control optimal control problems phase constraints Proof proper convex function Proposition proved quadratic form relation satisﬁes sequence solution subdifferential subset subspace sufﬁcient suﬂicient summable theory topological space topology vector vector-valued function verify weakly Weierstrass zero