A new basis implementation for a mixed order boundary value ODE solver
SIAM Journal on Scientific and Statistical Computing
Trust region algorithms for optimization with nonlinear equality and inequality constraints
Trust region algorithms for optimization with nonlinear equality and inequality constraints
SIAM Journal on Numerical Analysis
An analysis of reduced Hessian methods for constrained optimization
Mathematical Programming: Series A and B
ACM Transactions on Mathematical Software (TOMS)
CUTE: constrained and unconstrained testing environment
ACM Transactions on Mathematical Software (TOMS)
Algorithm 755: ADOL-C: a package for the automatic differentiation of algorithms written in C/C++
ACM Transactions on Mathematical Software (TOMS)
Trust-Region Interior-Point SQP Algorithms for a Class of Nonlinear Programming Problems
SIAM Journal on Control and Optimization
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Numerical Experience with a Reduced Hessian Methodfor Large Scale Constrained Optimization
Computational Optimization and Applications
An Adaptive Nonlinear Least-Squares Algorithm
ACM Transactions on Mathematical Software (TOMS)
Trust-region methods
Computational Optimization and Applications
A Trust-Region Approach to the Regularization of Large-Scale Discrete Forms of Ill-Posed Problems
SIAM Journal on Scientific Computing
On the Global Convergence of a Filter--SQP Algorithm
SIAM Journal on Optimization
A New Matrix-Free Algorithm for the Large-Scale Trust-Region Subproblem
SIAM Journal on Optimization
SIAM Journal on Optimization
An Interior Point Algorithm for Large-Scale Nonlinear Programming
SIAM Journal on Optimization
Newton's Method for Large Bound-Constrained Optimization Problems
SIAM Journal on Optimization
On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization
SIAM Journal on Optimization
Global Convergence of a Trust-Region SQP-Filter Algorithm for General Nonlinear Programming
SIAM Journal on Optimization
A large-scale trust-region approach to the regularization of discrete ill-posed problems
A large-scale trust-region approach to the regularization of discrete ill-posed problems
Computational Biology and Chemistry
Parameter Estimation Using Metaheuristics in Systems Biology: A Comprehensive Review
IEEE/ACM Transactions on Computational Biology and Bioinformatics (TCBB)
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We describe a new algorithm for a class of parameter estimation problems, which are either unconstrained or have only equality constraints and bounds on parameters. Due to the presence of unobservable variables, parameter estimation problems may have non-unique solutions for these variables. These can also lead to singular or ill-conditioned Hessians and this may be responsible for slow or non-convergence of nonlinear programming (NLP) algorithms used to solve these problems. For this reason, we need an algorithm that leads to strong descent and converges to a stationary point. Our algorithm is based on Successive Quadratic Programming (SQP) and constrains the SQP steps in a trust region for global convergence. We consider the second-order information in three ways: quasi-Newton updates, Gauss-Newton approximation, and exact second derivatives, and we compare their performance. Finally, we provide results of tests of our algorithm on various problems from the CUTE and COPS sets.