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- W4300008332 abstract "Summary In realistic field history-matching problems uncertainty parameters are subject to upper- and lower bounds which must be satisfied. Violation of bounds (e.g., using a negative porosity or permeability in a grid-block) may result in unphysical solutions or the failure of simulations. The Gauss-Newton (GN) optimizer using a trust-region (TR) search method performs more efficiently and robustly than using a line-search method. The GN trust-region search optimizer requires solving a trust-region subproblem (GNTRS) iteratively. Given gradient and Hessian evaluated at the current best solution, the objective function can be approximated by a quadratic model of the search step. The global minimum of the quadratic model within a ball-shaped trust-region, which is the solution of the GNTRS, is used as the new search step for the next iteration. However, available methods to solve a GNTRS cannot correctly handle bound constraints. This paper introduces an iterative dimension-reduction procedure to solve the GNTRS with bound constraints, which involves the following three steps. First, an unconstrained GNTRS with n variables is solved and the solution is accepted if no bound is violated. Otherwise, at least one bound is violated, and the dimension of the problem is reduced to m by activating one or more violated bounds, according to the Karush-Kuhn-Tucker (KKT) conditions. Second, the gradient, Hessian, and trust region size are updated in the reduced subspace accordingly. Third, an unconstrained GNTRS with m variables is solved in the reduced subspace. We repeat the last two steps until no bound is violated. To achieve better performance, we devised several algorithms to update gradient, sensitivity matrix and Hessian in the reduced subspace adapted to the problem type: (1) using the full Hessian expression to solve the GNTRS directly for problems with more observed data, (2) applying the matrix inversion lemma for problems with the regularization term and with fewer observed data, and (3) applying the linear transformation approach for problems without the regularization term and with fewer observed data. The proposed new GNTRS solver is first validated on different synthetic problems with known solutions and then tested on a suite of realistic field history matching problems. Our numerical tests confirm that the newly proposed GNTRS solver outperforms other methods for handling bound constraints. In our testing the new solver finds the correct solutions in all cases – with the least CPU time – while other methods failed for some test problems." @default.
- W4300008332 created "2022-10-03" @default.
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- W4300008332 date "2022-01-01" @default.
- W4300008332 modified "2023-10-16" @default.
- W4300008332 title "Solving Gauss-Newton Trust Region Subproblem with Bound Constraints" @default.
- W4300008332 doi "https://doi.org/10.3997/2214-4609.202244007" @default.
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