From Penalty to Exact Augmented Lagrangians

Zdeněk Dostál ()
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Zdeněk Dostál: VŠB - Technical University Ostrava, National Super computer Center and Department of Applied Mathematics

Chapter 6 in Optimal Quadratic Programming and QCQP Algorithms with Case Studies, 2025, pp 123-142 from Springer

Abstract: Abstract We first introduce the penalty method as a tool for reducing the equality-constrained quadratic programming problem to an unconstrained one and show that increasing the penalty enforces the reduced feasibility error. Then, we apply the penalty method to the augmented Lagrangian and show that we can achieve the same feasibility error without penalization using a suitable value of Lagrangian multipliers. We examine the convergence of the resulting augmented Lagrangian method with the exact solution of auxiliary problems.

Date: 2025
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DOI: 10.1007/978-3-031-95167-1_6

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