  This paper discusses a class of two-block smooth large-scale optimization
problems with both linear equality and linear inequality constraints, which
have a wide range of applications, such as economic power dispatch, data
mining, signal processing, etc.Our goal is to develop a novel partially
feasible distributed (PFD) sequential quadratic optimization (SQO) method
(PFD-SQO method) for this kind of problems. The design of the method is based
on the ideas of SQO method and augmented Lagrangian Jacobian splitting scheme
as well as feasible direction method,which decomposes the quadratic
optimization (QO) subproblem into two small-scale QOs that can be solved
independently and parallelly. A novel disturbance contraction term that can be
suitably adjusted is introduced into the inequality constraints so that the
feasible step size along the search direction can be increased to 1. The new
iteration points are generated by the Armijo line search and the partially
augmented Lagrangian function that only contains equality constraints as the
merit function. The iteration points always satisfy all the inequality
constraints of the problem. The theoretical properties, such as global
convergence, iterative complexity, superlinear and quadratic rates of
convergence of the proposed PFD-SQO method are analyzed under appropriate
assumptions, respectively. Finally, the numerical effectiveness of the method
is tested on a class of academic examples and an economic power dispatch
problem, which shows that the proposed method is quite promising.
