On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization

@article{Lalee1998OnTI,
  title={On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization},
  author={Marucha Lalee and J. Nocedal and T. Plantenga},
  journal={SIAM J. Optim.},
  year={1998},
  volume={8},
  pages={682-706}
}
This paper describes a software implementation of Byrd and Omojokun's trust region algorithm for solving nonlinear equality constrained optimization problems. The code is designed for the efficient solution of large problems and provides the user with a variety of linear algebra techniques for solving the subproblems occurring in the algorithm. Second derivative information can be used, but when it is not available, limited memory quasi-Newton approximations are made. The performance of the… Expand
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References

SHOWING 1-10 OF 61 REFERENCES
Large-scale nonlinear constrained optimization using trust regions
This dissertation describes the theory, software implementation and numerical testing of an algorithm for solving smooth nonlinear constrained optimization problems. The algorithm is designed toExpand
A Trust Region Method for Nonlinear Programming Based on Primal Interior-Point Techniques
  • T. Plantenga
  • Mathematics, Computer Science
  • SIAM J. Sci. Comput.
  • 1998
TLDR
A new trust region method for solving large-scale optimization problems with nonlinear equality and inequality constraints, which employs interior-point techniques from linear programming, adapting them for more general nonlinear problems. Expand
Large-scale linearly constrained optimization
An algorithm for solving large-scale nonlinear programs with linear constraints is presented. The method combines efficient sparse-matrix techniques as in the revised simplex method with stableExpand
A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization
A global convergence theory for a class of trust-region algorithms for solving the equality constrained optimization problem is presented. This theory is sufficiently general that it holds for anyExpand
The Conjugate Gradient Method and Trust Regions in Large Scale Optimization
Algorithms based on trust regions have been shown to be robust methods for unconstrained optimization problems. All existing methods, either based on the dogleg strategy or Hebden-More iterations,Expand
A Trust Region Algorithm for Equality Constrained Minimization: Convergence Properties and Implementation
In unconstrained minimization, trust region algorithms use directions that are a combination of the quasi-Newton direction and the steepest descent direction, depending on the fit between theExpand
Projected quasi-Newton algorithm with trust region for constrained optimization
In Ref. 1, Nocedal and Overton proposed a two-sided projected Hessian updating technique for equality constrained optimization problems. Although local two-step Q-superlinear rate was proved, itsExpand
On a subproblem of trust region algorithms for constrained optimization
TLDR
It is proved that the Hessian of the Lagrangian has at most one negative eigenvalue, and an example is presented to show thatThe Hessian may have a negative eigensvalue when one constraint is inactive at the solution. Expand
Computing a Celis-Dennis-Tapia trust-region step for equality constrained optimization
  • Yin Zhang
  • Mathematics, Computer Science
  • Math. Program.
  • 1992
TLDR
Numerical results are presented indicating that the proposed algorithm is reliable, robust and has the potential to be used as a building block to construct trust-region algorithms for small-sized problems in constrained optimization. Expand
A trust region method based on interior point techniques for nonlinear programming
TLDR
This paper focuses on the primal version of the new algorithm, an algorithm for minimizing a nonlinear function subject to nonlinear inequality constraints, which applies sequential quadratic programming techniques to a sequence of barrier problems. Expand
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