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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Vydané v:Journal of optimization theory and applications Ročník 200; číslo 1; s. 404 - 427
Hlavní autori: Berra, Silvia, La Torraca, Alessandro, Benvenuto, Federico, Sommariva, Sara
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.01.2024
Springer Nature B.V
Predmet:
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
65L05
Projected Newton’s method
Box-constrained optimization
65K10
Chemical reaction network
Projected gradient descent
Nonnegative constraints
ISSN:0022-3239, 1573-2878
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Shrnutí: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.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-023-02323-z