A methodology for solving chemical equilibrium systems
Applied Mathematics and Computation
Chemical equilibrium systems as numerical test problems
ACM Transactions on Mathematical Software (TOMS)
An interior point potential reduction method for constrained equations
Mathematical Programming: Series A and B
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Test Examples for Nonlinear Programming Codes
Test Examples for Nonlinear Programming Codes
A Potential Reduction Newton Method for Constrained Equations
SIAM Journal on Optimization
An affine scaling trust-region approach to bound-constrained nonlinear systems
Applied Numerical Mathematics
STRSCNE: A Scaled Trust-Region Solver for Constrained Nonlinear Equations
Computational Optimization and Applications
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
An interior-point method for solving box-constrained underdetermined nonlinear systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Estimation of pump-curves using genetic algorithms
Proceedings of the 10th annual conference on Genetic and evolutionary computation
Optimization Methods & Software
Robust Nonparametric Probability Density Estimation by Soft Clustering
ICANN '08 Proceedings of the 18th international conference on Artificial Neural Networks, Part I
A Gauss-Newton method for solving bound-constrained underdetermined nonlinear systems
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART II
Trust-region quadratic methods for nonlinear systems of mixed equalities and inequalities
Applied Numerical Mathematics
A superlinearly convergent projection method for constrained systems of nonlinear equations
Journal of Global Optimization
Spectral gradient projection method for monotone nonlinear equations with convex constraints
Applied Numerical Mathematics
RTL power modeling and estimation of sleep transistor based power gating
Journal of Embedded Computing - PATMOS 2007 selected papers on low power electronics
An interior-point method for solving box-constrained underdetermined nonlinear systems
Journal of Computational and Applied Mathematics
Hybrid RSS-RTT localization scheme for indoor wireless networks
EURASIP Journal on Advances in Signal Processing
A Levenberg-Marquardt algorithm for unconstrained multicriteria optimization
Operations Research Letters
RTL power modeling and estimation of sleep transistor based power gating
PATMOS'07 Proceedings of the 17th international conference on Integrated Circuit and System Design: power and timing modeling, optimization and simulation
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We consider the problem of finding a solution of a constrained (and not necessarily square) system of equations, i.e., we consider systems of nonlinear equations and want to find a solution that belongs to a certain feasible set. To this end, we present two Levenberg-Marquardt-type algorithms that differ in the way they compute their search directions. The first method solves a strictly convex minimization problem at each iteration, whereas the second one solves only one system of linear equations in each step. Both methods are shown to converge locally quadratically under an error bound assumption that is much weaker than the standard nonsingularity condition. Both methods can be globalized in an easy way. Some numerical results for the second method indicate that the algorithm works quite well in practice.