A Unified Approach to Global Convergence of Trust-Region Methods for Nonsmooth Optimization
RICE UNIV HOUSTON TX DEPT OF COMPUTATIONAL AND APPLIED MATHEMATICS
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This paper investigates the global convergence of trust region TR methods for solving nonsmooth minimization problems. For a class of nonsmooth objective functions called regular functions, conditions are found on the TR local models that imply three fundamental convergence properties. These conditions are shown to be satisfied by appropriate forms of Fletchers TR method for solving constrained optimization problems, Powell and Yuans TR method for solving nonlinear fitting problems, Zhang, Kim and Lasdons successive linear programming method for solving constrained problems, Duff, Nocedal and Reids TR method for solving systems of nonlinear equations, and El Hallabi and Tapias TR method for solving systems of nonlinear equations. Thus our results can be viewed as a unified convergence theory for TR methods for nonsmooth problems.
- Numerical Mathematics
- Operations Research