A double-step-length symmetric splitting sequential quadratic optimization algorithm for two-block nonconvex optimization

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