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A sparse nonlinear optimization algorithm

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One of the most effective numerical techniques for solving nonlinear programming problems is the sequential quadratic programming approach. Many large nonlinear programming problems arise naturally in data fitting and when discretization techniques are applied to systems described by ordinary or partial differential equations. Problems of this type are characterized by matrices which are large and sparse. This paper describes a nonlinear programming algorithm which exploits the matrix sparsity produced by these applications. Numerical experience is reported for a collection of trajectory optimization problems with nonlinear equality and inequality constraints.

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The authors wish to acknowledge the insightful contributions of Dr. William Huffman.

Communicated by H. Y. Huang

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Betts, J.T., Frank, P.D. A sparse nonlinear optimization algorithm. J Optim Theory Appl 82, 519–541 (1994).

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Key Words

  • Sparse nonlinear programming
  • sequential quadratic programming
  • trajectory optimization