Solving Problems With Inconsistent Constraints With a Modified Augmented Lagrangian Method

We present a numerical method for the minimization of constrained optimization problems where objective is augmented with large quadratic penalties inconsistent equality constraints. Such objectives arise from integral penalty methods direct transcription optimal control problems. The Lagrangian (ALM) has number advantages over (QPM). However, if constraints are inconsistent, then ALM might not converge to point that minimizes bias and term. Therefore, we modification fits our purpose. prove convergence modified bound its local rate by unmodified method. Numerical experiments demonstrate can minimize certain functions faster than QPM, whereas converges minimizer significantly different problem.