Asymptotology of Chemical Reaction Networks

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.Comment: 23 pages, 8 figures, 84 refs, Corrected Journal Versio

A Newton-type method for quadratic programming problem and variational equilibrium problem

The active-set Newton method developed earlier by the author and her supervisor for mixed complementarity problems is applied to solving the quadratic programming problem with a positive definite matrix of the objective function and for variational equilibrium problem. A theoretical justification is given to the fact that the method is guaranteed to find the exact solution in a finite number of steps. Numerical results indicate that this approach is competitive with other available methods as for quadratic programming problems and for variational equilibrium problem. © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 13th International Symposium “Intelligent Systems” (INTELS'18)