A symmetric splitting sequential quadratic optimization algorithm for two-block nonlinearly constrained nonconvex optimization

In this paper, a double-step-length symmetric splitting sequential quadratic optimization (DSL-SS-SQO) algorithm for solving two-block nonconvex with nonlinear constraints is proposed. First, at each iteration, the idea of embedded into (QO) subproblem approximating discussed problem. As result, QO split two small-scale QOs, which can generate improved search directions primal variables. Second, augmented Lagrangian function used as merit function, and step sizes are yielded by performing Armijo line along directions. Third, under mild conditions, global convergence, strong iterative complexity, Maratos effect DSL-SS-SQO proven. Finally, some numerical results reported, comparisons obtained IPOPT solver also provided, preliminarily show that proposed promising.