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Nonmonotone Trust Region Methods for Nonlinear Equality Constrained Optimization without a Penalty Function (2000)
| Content Provider | CiteSeerX |
|---|---|
| Author | Ulbrich, Michael Ulbrich, Stefan |
| Abstract | We propose and analyze a class of penalty-function-free nonmonotone trust-region methods for nonlinear equality constrained optimization problems. The algorithmic framework yields global convergence without using a merit function and allows nonmonotonicity independently for both, the constraint violation and the value of the Lagrangian function. Similar to the Byrd--Omojokun class of algorithms, each step is composed of a quasinormal and a tangential step. Both steps are required to satisfy a decrease condition for their respective trust-region subproblems. The proposed mechanism for accepting steps combines nonmonotone decrease conditions on the constraint violation and/or the Lagrangian function, which leads to a flexibility and acceptance behavior comparable to filter-based methods. We establish the global convergence of the method. Furthermore, transition to quadratic local convergence is proved. Numerical tests are presented that confirm the robustness and efficiency of the approach. |
| File Format | |
| Journal | MATH. PROGRAM., SER. B |
| Language | English |
| Publisher Date | 2000-01-01 |
| Access Restriction | Open |
| Subject Keyword | Penalty Function Nonmonotone Trust Region Method Nonlinear Equality Constrained Optimization Decrease Condition Constraint Violation Lagrangian Function Respective Trust-region Subproblems Nonlinear Equality Global Convergence Penalty-function-free Nonmonotone Trust-region Method Filter-based Method Acceptance Behavior Optimization Problem Byrd Omojokun Class Quadratic Local Convergence Tangential Step Algorithmic Framework Yield Global Convergence Numerical Test Step Combine Merit Function |
| Content Type | Text |
| Resource Type | Article |
