On the Finite Complexity of Solutions in a Degenerate System of Quadratic Equations: Exact Formula

Abstract

The paper describes an application of the p-regularity theory to Quadratic Programming (QP) and nonlinear equations with quadratic mappings. In the first part of the paper, a special structure of the nonlinear equation and a construction of the 2-factor operator are used to obtain an exact formula for a solution to the nonlinear equation. In the second part of the paper, the QP problem is reduced to a system of linear equations using the 2-factor operator. The solution to this system represents a local minimizer of the QP problem along with its corresponding Lagrange multiplier. An explicit formula for the solution of the linear system is provided. Additionally, the paper outlines a procedure for identifying active constraints, which plays a crucial role in constructing the linear system.