Convergence properties of trust region methods for linear and convex constraints
We develop a convergence theory for convex and linearly constrained trust region methods which only requires that the step between iterates produce a sufficient reduction in the trust region subproblem. Global convergence is established for a general convex minimization problem while the local analysis is for linearly constrained problems. The main local result establishes that if the sequence converges to a nondegenerate stationary point then the active constraints at the solution are identified in a finite number of iterations. As a consequence of the identification properties, we develop rate of convergence results by assuming that the step is a truncated Newton method. Our development is mainly geometrical; this approach allows the development of a convergence theory without any linear independence assumptions. 20 refs., 1 fig.
- Research Organization:
- Argonne National Lab., IL (USA)
- DOE Contract Number:
- W-31109-ENG-38
- OSTI ID:
- 6929897
- Report Number(s):
- ANL/MCS-TM-116; ON: DE88013608
- Country of Publication:
- United States
- Language:
- English
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