Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function

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 viol...

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Bibliographic Details
Published in:Mathematical programming Vol. 95; no. 1; pp. 103 - 135
Main Authors: Ulbrich, M., Ulbrich, S.
Format: Journal Article Conference Proceeding
Language:English
Published: Heidelberg Springer 01.01.2003
Springer Nature B.V
Subjects:
Algorithms
Applied sciences
Digital Object Identifier
Exact sciences and technology
Mathematical programming
Methods
Operational research and scientific management
Operational research. Management science
Optimization
Quadratic programming
local convergence
global convergence
Non linear programming
Quadratic programming
equality constraints
Constrained optimization
Penalty function
large-scale optimization
Sequential method
Equality constraint
nonmonotone trust-region methods
Lagrangian function
sequential quadratic programming
Numerical convergence
Mathematical programming
Trust region method
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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 quasi-normal 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.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-002-0343-9