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- W2000403767 abstract "An iterative method is described for the minimization of a continuously differentiable function F(x) of n variables subject to linear inequality constraints. Without any convexity or second-order derivative assumptions it is shown that every cluster point of the sequence { x j } constructed by the method is a stationary point. The method constructs sets of directions which are approximately conjugate. At appropriate points a special step is performed which utilizes the second-order information of the previous conjugate directions to accelerate the rate of convergence. If z is a cluster point of { x j } and F(x) is twice continuously differentiable in some neighborhood of z and the Hessian matrix of F(x) has certain properties, then { x j } converges to z and the rate of convergence is ( n − q )-step superlinear, where q is the number of constraints which are active at z . Furthermore, if the Hessian matrix of F(x) satisfies a Lipschitz condition in a neighborhood of z then as a result of the accelerated step, the rate of convergence of { x j } will be ( n−q +1)-step cubic." @default.
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- W2000403767 date "1975-12-01" @default.
- W2000403767 modified "2023-10-16" @default.
- W2000403767 title "An accelerated conjugate direction method to solve linearly constrained minimization problems" @default.
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- W2000403767 doi "https://doi.org/10.1016/s0022-0000(75)80055-9" @default.
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