1. On the use of piecewise linear models in nonlinear programming.
- Author
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Byrd, Richard, Nocedal, Jorge, Waltz, Richard, and Wu, Yuchen
- Subjects
LINEAR statistical models ,NONLINEAR programming ,ALGORITHMS ,SET theory ,MATHEMATICAL optimization ,QUADRATIC programming ,APPROXIMATION theory ,LAGRANGE equations - Abstract
This paper presents an active-set algorithm for large-scale optimization that occupies the middle ground between sequential quadratic programming and sequential linear-quadratic programming methods. It consists of two phases. The algorithm first minimizes a piecewise linear approximation of the Lagrangian, subject to a linearization of the constraints, to determine a working set. Then, an equality constrained subproblem based on this working set and using second derivative information is solved in order to promote fast convergence. A study of the local and global convergence properties of the algorithm highlights the importance of the placement of the interpolation points that determine the piecewise linear model of the Lagrangian. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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