Computing Optimal Locally Constrained Steps
SIAM Journal on Scientific and Statistical Computing1981Vol. 2(2), pp. 186–197
Citations Over TimeTop 10% of 1981 papers
Abstract
In seeking to solve an unconstrained minimization problem, one often computes steps based on a quadratic approximation q to the objective function. A reasonable way to choose such steps is by minimizing q constrained to a neighborhood of the current iterate. This paper considers ellipsoidal neighborhoods and presents a new way to handle certain computational details when the Hessian of q is indefinite, paying particular attention to a special case which may then arise. The proposed step computing algorithm provides an attractive way to deal with negative curvature. Implementations of this algorithm have proved very satisfactory in the nonlinear least-squares solves NL2SOL.
Related Papers
- → Superlinearly Convergent Trust-Region Method without the Assumption of Positive-Definite Hessian(2006)3 cited
- → A practical trust region method for equality constrained optimization problems(1993)1 cited
- NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION(2004)
- NONMONOTONIC TRUST REGION PROJECTED REDUCED HESSIAN ALGORITHM WITH TWO-PIECE UPDATE FOR CONSTRAINED OPTIMIZATION(2004)