Ali Baharev

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Multiple steady states are typically discovered by tracing a solution path, including turning points. A new technique is presented here that does not follow this approach. The original problem is solved directly, without tracing a solution path. The proposed branch and prune algorithm is guaranteed to find all solutions automatically. Core components of the(More)
The need of reliably solving systems of nonlinear equations often arises in the everyday practice of chemical engineering. In general, standard methods cannot provide theoretical guarantee for convergence to a solution, cannot reliably find multiple solutions, and cannot prove non-existence of solutions. Interval methods provide tools to overcome these(More)
A method is proposed that either returns all solutions to steady-state models of distillation columns or proves infeasibility. No initial estimates are required. The computational effort grows linearly with the number of stages. Successful solution of a numerically challenging reactive distillation column with 7 steady-states show the robustness of the(More)
; and Sándor Kemény is professor at the same institution (email: The authors wish to thank Mr. Richárd Király for his preliminary work. The authors are grateful to the Associate Editor of STCO and the unknown reviewers for their helpful suggestions. 2 ABSTRACT AND KEY WORDS Unfortunately many of the numerous algorithms for computing the(More)
Interval arithmetic can be successfully applied to find all the solutions of systems of nonlinear equations in a given region with mathematical certainty. Not finding any solution means non-existence of solutions in the studied region. The mathematical certainty, provided by the method, makes interval arithmetic a powerful tool for solving problems from the(More)
A general framework is presented for finding all solutions to systems of nonlinear equations, or proving that there is no solution to the problem. Components of this framework are interval arithmetic, affine arithmetic, constraint propagation based on directed acyclic graph (DAG) representation of the problem, a pruning technique based on linear programming(More)