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115         << "Ceres bug: NextDirection() called on L-BFGS after inverse Hessian "
129 LOG(WARNING) << "Numerical failure in L-BFGS update: inverse Hessian "
155 << " parameters, this will allocate a dense approximate inverse Hessian"
170 << "Ceres bug: NextDirection() called on BFGS after inverse Hessian "
183 // Hessian at the k+1-th iteration, s_k = (x_{k+1} - x_{k}) and
184 // y_k = (grad_{k+1} - grad_{k}). As the approximated Hessian must be
198 // to update the Hessian approximation if:
204 // information in the Hessian. For example going from 1e-10 -> 1e-14
219 // Update dense inverse Hessian approximation.
222 // Rescale the initial inverse Hessian approximation (H_0) to be
224 // inverse Hessian at the start point. As shown in [1]:
234 // of the true initial Hessian (not the inverse) respectively. Thus,
235 // \gamma is an approximate eigenvalue of the true inverse Hessian, and
237 // similar scale to the true inverse Hessian. This technique is widely
259 << "Hessian approximation.";
311 // Finally, update inverse Hessian approximation according to:
323 LOG(WARNING) << "Numerical failure in BFGS update: inverse Hessian "