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- Ali Baharev, Lubomir Kolev, Endre Rév
- 2010

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, Endre Rév
- 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)

- Ali Baharev, Arnold Neumaier
- 2014

A globally convergent method is proposed that either returns all solutions to steady-state models of distillation columns or proves their infeasibility. Initial estimates are not required. The method requires a specific but fairly general block-sparsity pattern; in return, the computational efforts grow linearly with the number of stages in the column. The… (More)

- Ali Baharev, Tobias Achterberg, Endre Rév
- 2009

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)

- 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)

; 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, Arnold Neumaier
- 2012

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
- 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)

- Ali Baharev, Ferenc Domes, Arnold Neumaier
- Numerical Algorithms
- 2016

Tearing is a long-established decomposition technique, widely adapted across many engineering fields. It reduces the task of solving a large and sparse nonlinear system of equations to that of solving a sequence of low-dimensional ones. The most serious weakness of this approach is well-known: It may suffer from severe numerical instability. The present… (More)

- Ali Baharev, Ferenc Domes, Arnold Neumaier
- 2015

This paper focuses on finding all solutions to nonlinear algebraic systems of equations in a given domain. First, scattered points are computed that can be considered as a representative sample of the solution manifold of a given underdetermined nonlinear system of equations. If this underdetermined system is then augmented by further equations such that… (More)