Abstract
We propose a sparsity preserving algorithm for solving large-scale, nonlinear programming problems. The algorithm solves at each iteration a subproblem, which contains a linearized objective function augmented by a simple quadratic term and linearized constraints. The quadratic term added to the linearized objective function plays the role of step restriction which is essential in ensuring global convergence of the algorithm. If the conjugate gradient method or successive over-relaxation method is used to solve the subproblems, the sparsity of the original problem is preserved, because those methods only require simple operations on the rows of the constraint matrix. Thus, large-scale problems can be dealt with when the constraint matrices are sparse enough to be stored in a compact form. Practical implementation of the algorithm is described and computational results are reported.
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Fukushima, M., Takazawa, K., Ohsaki, S. et al. Successive linearization methods for large-scale nonlinear programming problems. Japan J. Indust. Appl. Math. 9, 117–132 (1992). https://doi.org/10.1007/BF03167197
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DOI: https://doi.org/10.1007/BF03167197