This study presents a modified primal-dual interior point method (MPD-IPM) for solving convex quadratic optimization problems. The modification is performed through linearization of the central path and the introduction of an improved initialization strategy derived from the derivative structure of the Lagrangian function, unlike the classical approach, whose iterates follow a nonlinear trajectory. The proposed formulation generates linearized subsidiary constraint equations that reduce curvature effects during path-following. Numerical experiments conducted on benchmark and hypothetically generated problems demonstrate improved iteration counts, enhanced convergence reliability, and reduced computational time, particularly for large-scale instances.
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