Sequential systems of linear equations algorithm for nonlinear optimization problems with general constraints. (English) Zbl 0892.90163
Summary: In another paper of the authors [yet unpublished] a new superlinearly convergent algorithm of sequential systems of linear equations (SSLE) for nonlinear optimization problems with inequality constraints was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 the paper mentioned above it was 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 has to perform a pivoting operation to adjust the penalty parameter per iteration. In this paper, we improve this work and present a new algorithm for sequential systems of linear equations and 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; superlinearly convergent algorithm; inequality constraintsReferences:
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