Work

A Galerkin Approach to the Generalized Karush–Kuhn–Tucker Conditions for the Solution of an Elliptic Distributed Optimal Control Problem with Pointwise State and Control Constraints

Year: 2025

Type: article

Abstract: We develop a convergence analysis for the simplest finite element method for a model linear-quadratic elliptic distributed optimal control problem with pointwise control and state constraints under minimal assumptions on the constraint functions. We then derive the generalized Karush–Kuhn–Tucker conditions for the solution of the optimal control problem from the convergence results of the finite element method and the Karush–Kuhn–Tucker conditions for the solutions of the discrete problems.

Source: Computational Methods in Applied Mathematics

DOI: 10.1515/cmam-2025-0007

Authors: Susanne C. Brenner, Li-Yeng Sung

Institution: Louisiana State University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Finite Element Methods for Elliptic Least-Squares Problems with Inequality Constraints