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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)

- Ali Baharev
- 2008

Computing the steady state of multistage counter-current processes like distillation, extraction, or absorption is the equivalent to finding solutions for large scale non-linear equation systems. The conventional solution techniques are fast and efficient if a good estimation is available but are prone to fail, and do not provide information about 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)

- Ali Baharev, Sándor Kemény
- Statistics and Computing
- 2008

; and Sándor Kemény is professor at the same institution (email: kemeny@mail.bme.hu). 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)

- Ali Baharev, Endre Rév
- 2008

Solving general nonlinear systems of equations and/or finding the global optimum of nonconvex functions constitute an important part of the everyday practice in chemical engineering. Standard methods cannot provide theoretical guarantee for convergence to a solution, cannot find multiple solutions, and cannot prove non-existence of solutions. This is 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)

Chemical process models are highly structured. Information on how the hierarchical components are connected helps to solve the model efficiently. Our ultimate goal is to develop structure-driven optimization methods for solving nonlinear programming problems (NLP). The structural information retrieved from the JModelica environment will play an important… (More)

- Ali Baharev, Endre Rév, +14 authors John K. Reid
- 2009

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)

- Ali Baharev
- 2009

The need of reliably solving large-scale system of nonlinear equations often arises in the everyday practice of chemical engineering. The following difficulties can occur when performing these calculations with standard methods. (a) It remains unknown whether the problem is indeed infeasible or just the initial points were poor if the iteration fails after… (More)