An Algorithm Based on the Modified Sufficient Conditions of the Inertia-Controlling Method for the Global Solution of a General Quadratic Problem

In this paper, we consider a general quadratic problem (P) with linear constraints that are not necessarily linear independent. To resolve this problem, we use a new algorithm based on the Inertia-Controlling method while replacing the condition of the Lagrange multiplier vector μ by resolution of a linear system obtained thanks to the Kuruch–Kuhn–Tuker matrix (KKT-matrix) in order to determine the minimizing direction of (P) and so calculate the steep length in general cases, as follows: indefinite, concave, and convex cases. This paper has an interesting topic and meaningful results.