## Davidon-Broyden Rank-one Minimization Methods in Hilbert Space with Application to Optimal Control Problems |

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ansn APPLICATION TO OPTIMAL applied basic algorithm bounded set Broyden ref choice choosing the step chosen by method class of minimization Class of Rank-One conjugate gradient method convex hull Corollary Davidon-Broyden Class denote DFP algorithm DFP method element of H equation 12 Euclidean spaces example problem Figure finite number form a Schauder functional evaluations given by equation Goldfarb ref Hence Horwitz and Sarachik ieN(n infinite-dimensional real Hilbert J(un J(xn Langley Research Center lemma mathematical induction methods of choosing minimum monotone sequence Moreover Number of functional number of steps one-dimensional minimization operator from H optimal control problem positive self-adjoint linear Proof quadratic functional quasi-Newton methods Quasi-Newton Minimization Methods rank-one algorithms rate of convergence real Hilbert space real numbers sample optimal control Sarachik ref Schauder basis self-adjoint operator SPACE WITH APPLICATION steepest descent strongly positive self-adjoint theorem tion v(n+l variables x e H x,Ax