An Algorithm for Solving Quadratic Optimization Problems with Nonlinear Equality Constraints

TL;DR

This paper introduces a new efficient algorithm for solving quadratic optimization problems with nonlinear equality constraints, offering convergence guarantees and demonstrating effectiveness in practical applications like ellipse fitting and electrical machine control.

Contribution

The paper proposes a novel computationally efficient algorithm for quadratic optimization with nonlinear equality constraints, with proven local convergence to KKT solutions.

Findings

Algorithm converges locally to KKT solutions

Effective in ellipse fitting applications

Demonstrated success in electrical machine control

Abstract

The classical method to solve a quadratic optimization problem with nonlinear equality constraints is to solve the Karush-Kuhn-Tucker (KKT) optimality conditions using Newton's method. This approach however is usually computationally demanding, especially for large-scale problems. This paper presents a new computationally efficient algorithm for solving quadratic optimization problems with nonlinear equality constraints. It is proven that the proposed algorithm converges locally to a solution of the KKT optimality conditions. Two relevant application problems, fitting of ellipses and state reference generation for electrical machines, are presented to demonstrate the effectiveness of the proposed algorithm.