Solving problems with inconsistent constraints with a modified augmented lagrangian method
| Autor: | Martin P. Neuenhofen, Eric C. Kerrigan |
|---|---|
| Rok vydání: | 2022 |
| Předmět: |
0906 Electrical and Electronic Engineering
Industrial Engineering & Automation Optimization and Control (math.OC) Control and Systems Engineering 0102 Applied Mathematics FOS: Mathematics Electrical and Electronic Engineering Mathematics - Optimization and Control Computer Science::Numerical Analysis Computer Science Applications 0913 Mechanical Engineering |
| Popis: | We present a numerical method for the minimization of constrained optimization problems where the objective is augmented with large quadratic penalties of inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM). However, if the equality constraints are inconsistent, then ALM might not converge to a point that minimizes the bias of the objective and penalty term. Therefore, we present a modification of ALM that fits our purpose. We prove convergence of the modified method and bound its local convergence rate by that of the unmodified method. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem. Comment: 8 pages. 3 figures. 4 tables |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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