Sequential Systems of Linear Equations Algorithm for Nonlinear Optimization Problems with General Constraints

Z. Y. Gao, G. P. He and F. Wu
Additional contact information
Z. Y. Gao: Northern Jiaotong University
G. P. He: Academia Sinica
F. Wu: Academia Sinica

Journal of Optimization Theory and Applications, 1997, vol. 95, issue 2, No 7, 397 pages

Abstract: Abstract In Ref. 1, a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was proposed. At each iteration, this new algorithm only needs to solve four systems of linear equations having the same coefficient matrix, which is much less than the amount of computation required for existing SQP algorithms. Moreover, unlike the quadratic programming subproblems of the SQP algorithms (which may not have a solution), the subproblems of the SSLE algorithm are always solvable. In Ref. 2, it is shown that the new algorithm can also be used to deal with nonlinear optimization problems having both equality and inequality constraints, by solving an auxiliary problem. But the algorithm of Ref. 2 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve the work of Ref. 2 and present a new algorithm of sequential systems of linear equations for general nonlinear optimization problems. This new algorithm preserves the advantages of the SSLE algorithms, while at the same time overcoming the aforementioned shortcomings. Some numerical results are also reported.

Keywords: Optimization; general constraints; algorithms; sequential systems of linear equations; coefficient matrices; superlinear convergence (search for similar items in EconPapers)
Date: 1997
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1023/A:1022639306130

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