Reduced SQP implementation for large-scale optimization problems

Abstract: "The development and implementation of the Range and Null space Decomposition (RND) strategy for large-scale problems is described with emphasis on the optimization of engineering systems. The RND technique, as detailed in Vasantharajan and Biegler (1988), uses nonorthonormal, gradient based projections for the Jacobian. However, this implementation is dense, and does not take advantage of system sparsity. Here we extend this algorithm to incorporate general purpose sparse matrix techniques. Also, problems like inconsistent linearizations and infeasible Quadratic Programs (QPs), which are generally associated with QP based methods compromise the robustness of this method and need to be considered.Finally, systematic ways of generating a nonsingular basis for general nonlinear programs must be developed if this strategy is to be adapted to solve large, sparse problems efficiently. To deal with these problems, a two phase LP-based procedure is coupled to the RND algorithm. This strategy also serves to partition the variables into decisions and dependents, thereby generating a nonsingular basis. Any redundancies/degeneracies in the constraints are also detected and processed separately. The entire reduced SQP implementation is then interfaced with GAMS (Brooke et al. (1988)), a front end for representing and solving process models.Finally, a thorough comparison of the RND based reduced SQP strategy with MINOS (Murtagh and Saunders (1978)) is effected on a set of NLPs and process design problems. The process problems include the optimization of the operation of distillation columns. These problems warrant special mention as have been uniquely conceived and implemented in a novel equation-oriented manner, thus exploiting the full potential of the GAMS architecture. Detailed discussion of the formulation and results are included and results are obtained that confirm the viability and efficacy of the reduced SQP implementation for efficient solution of large, difficult nonlinear programs."