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This paper discusses a class of two-block smooth large-scale optimizationproblems with both linear equality and linear inequality constraints, whichhave a wide range of applications, such as economic power dispatch, datamining, signal processing, etc.Our goal is to develop a novel partiallyfeasible distributed (PFD) sequential quadratic optimization (SQO) method(PFD-SQO method) for this kind of problems. The design of the method is basedon the ideas of SQO method and augmented Lagrangian Jacobian splitting schemeas well as feasible direction method,which decomposes the quadraticoptimization (QO) subproblem into two small-scale QOs that can be solvedindependently and parallelly. A novel disturbance contraction term that can besuitably adjusted is introduced into the inequality constraints so that thefeasible step size along the search direction can be increased to 1. The newiteration points are generated by the Armijo line search and the partiallyaugmented Lagrangian function that only contains equality constraints as themerit function. The iteration points always satisfy all the inequalityconstraints of the problem. The theoretical properties, such as globalconvergence, iterative complexity, superlinear and quadratic rates ofconvergence of the proposed PFD-SQO method are analyzed under appropriateassumptions, respectively. Finally, the numerical effectiveness of the methodis tested on a class of academic examples and an economic power dispatchproblem, which shows that the proposed method is quite promising.

A Partially Feasible Distributed SQO Method for Two-block General Linearly Constrained Smooth Optimization