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A unique non-linear optimization program for exact real-time optimal dispatching with security constraints is presented. The basic optimization technique employs complex Lagrange multipliers and an innovative slack variable approach. The program was designed specifically for real-time application but can also be used off-line for optimal power flow solutions. Fundamental to the technique is a new Hessian matrix approximation, called a Diflex Hessian, which preserves sparsity and saves considerable computer core memory over the conventional Hessian. The Diflex Hesslan is derived in a unique mathematical style which was instrumental in its development. Other novel techniques of sparse matrix elimination and optimization are also described including unique logic for inequality constraint switching. Test results on a 1200-bus model are presented and indicate computer core memory and time requirements are comparable to a Newton power flow solution.