Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks
In this work, we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large-scale systems of quadratic autonomous ordinary differential equations (ODE) modeling, e.g., the dynamic of complex chemical reaction networks. Toward this aim,...
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| Published in: | Journal of optimization theory and applications Vol. 200; no. 1; pp. 404 - 427 |
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| Main Authors: | , , , |
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| Language: | English |
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01.01.2024
Springer Nature B.V |
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| ISSN: | 0022-3239, 1573-2878 |
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| Abstract | In this work, we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large-scale systems of quadratic autonomous ordinary differential equations (ODE) modeling, e.g., the dynamic of complex chemical reaction networks. Toward this aim, we reformulate the problem as a box-constrained optimization problem where the roots of a set of nonlinear equations need to be determined. Then, we propose to use a projected Newton’s approach combined with a gradient descent algorithm so that every limit point of the sequence generated by the overall algorithm is a stationary point. More importantly, we suggest replacing the standard orthogonal projector with a novel operator that ensures the final solution to satisfy the box constraints while lowering the probability that the intermediate points reached at each iteration belong to the boundary of the box where the Jacobian of the objective function may be singular. The effectiveness of the proposed approach is shown in a practical scenario concerning a chemical reaction network modeling the signaling network of colorectal cancer cells. Specifically, in this scenario the proposed algorithm is proved to be faster and more accurate than a classical dynamical approach where the asymptotically stable states are computed as the limit points of the flux of the Cauchy problem associated with the ODE system. |
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| AbstractList | In this work, we present a fast, globally convergent, iterative algorithm for computing the asymptotically stable states of nonlinear large-scale systems of quadratic autonomous ordinary differential equations (ODE) modeling, e.g., the dynamic of complex chemical reaction networks. Toward this aim, we reformulate the problem as a box-constrained optimization problem where the roots of a set of nonlinear equations need to be determined. Then, we propose to use a projected Newton’s approach combined with a gradient descent algorithm so that every limit point of the sequence generated by the overall algorithm is a stationary point. More importantly, we suggest replacing the standard orthogonal projector with a novel operator that ensures the final solution to satisfy the box constraints while lowering the probability that the intermediate points reached at each iteration belong to the boundary of the box where the Jacobian of the objective function may be singular. The effectiveness of the proposed approach is shown in a practical scenario concerning a chemical reaction network modeling the signaling network of colorectal cancer cells. Specifically, in this scenario the proposed algorithm is proved to be faster and more accurate than a classical dynamical approach where the asymptotically stable states are computed as the limit points of the flux of the Cauchy problem associated with the ODE system. |
| Author | Benvenuto, Federico Berra, Silvia La Torraca, Alessandro Sommariva, Sara |
| Author_xml | – sequence: 1 givenname: Silvia surname: Berra fullname: Berra, Silvia organization: Dipartimento di Matematica, Università di Genova – sequence: 2 givenname: Alessandro surname: La Torraca fullname: La Torraca, Alessandro organization: Data and Analytics Chapter, Roche S.p.A – sequence: 3 givenname: Federico surname: Benvenuto fullname: Benvenuto, Federico organization: Dipartimento di Matematica, Università di Genova – sequence: 4 givenname: Sara orcidid: 0000-0003-1835-9399 surname: Sommariva fullname: Sommariva, Sara email: sommariva@dima.unige.it organization: Dipartimento di Matematica, Università di Genova |
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| CitedBy_id | crossref_primary_10_1109_OJPEL_2025_3604475 crossref_primary_10_1038_s41598_024_67862_5 crossref_primary_10_1016_j_mex_2024_102865 |
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| Keywords | 65L05 Projected Newton’s method Box-constrained optimization 65K10 Chemical reaction network Projected gradient descent Nonnegative constraints |
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| SubjectTerms | Algorithms Applications of Mathematics Asymptotic properties Calculus of Variations and Optimal Control; Optimization Cauchy problems Chemical reactions Colorectal cancer Constraints Differential equations Engineering Iterative algorithms Iterative methods Mathematical models Mathematics Mathematics and Statistics Modelling Newton methods Nonlinear equations Nonlinear systems Operations Research/Decision Theory Operators (mathematics) Optimization Ordinary differential equations Original Paper Theory of Computation |
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| Title | Combined Newton-Gradient Method for Constrained Root-Finding in Chemical Reaction Networks |
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