Monotone Splitting Sequential Quadratic Optimization Algorithm with Applications in Electric Power Systems

Abstract

In this paper, we propose a new sequential quadratic optimization algorithm for solving two-block nonconvex optimization with linear equality and generalized box constraints. First, the idea of the splitting algorithm is embedded in the method for solving the quadratic optimization approximation subproblem of the discussed problem, and then, the subproblem is decomposed into two independent low-dimension quadratic optimization subproblems to generate a search direction for the primal variable. Second, a deflection of the steepest descent direction of the augmented Lagrangian function with respect to the dual variable is considered as the search direction of the dual variable. Third, using the augmented Lagrangian function as the merit function, a new primal–dual iterative point is generated by Armijo line search. Under mild conditions, the global convergence of the proposed algorithm is proved. Finally, the proposed algorithm is applied to solve a series of mid-to-large-scale economic dispatch problems for power systems. Comparing the numerical results demonstrates that the proposed algorithm possesses superior numerical effects and good robustness.