Design and Implementation of a Reduced-Space SQP Solver with Column Reordering for Large-Scale Process Optimization

Process industries increasingly face large-scale nonlinear programs with high dimensionality and tight constraints. This study reports on the design and implementation of a reduced-space sequential quadratic programming (RSQP) solver for such settings. The solver couples a column-reordering space-decomposition strategy with sparse-matrix storage/kernels, and is implemented in a modular C++ framework that supports range/null-space splitting, line search, and convergence checks. We evaluate six small-scale benchmarks with non-convex/exponential characteristics, a set of variable-dimension tests up to 128 k variables, and an industrial reverse-osmosis (RO) optimization. On small problems, RSQP attains an accuracy comparable to a full-space sequential quadratic programming (SQP) baseline. In variable-dimension tests, the solver shows favorable scaling when moving from 64 k to 128 k variables; under dynamically varying degrees of freedom, the iteration count decreases by about 62% with notable time savings. In the RO case, daily operating cost decreases by 4.98% and 1.46% across two scenarios while satisfying water-quality constraints. These results indicate that consolidating established RSQP components with column reordering and sparse computation yields a practical, scalable solver for large-scale process optimization.