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A reduced Hessian SQP method for inequality constrained optimization

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Abstract

This paper develops a reduced Hessian method for solving inequality constrained optimization problems. At each iteration, the proposed method solves a quadratic subproblem which is always feasible by introducing a slack variable to generate a search direction and then computes the steplength by adopting a standard line search along the direction through employing the l ∞ penalty function. And a new update criterion is proposed to generate the quasi-Newton matrices, whose dimensions may be variable, approximating the reduced Hessian of the Lagrangian. The global convergence is established under mild conditions. Moreover, local R-linear and superlinear convergence are shown under certain conditions.

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Authors and Affiliations

  1. College of Mathematics and Econometrics, Hunan University, Changsha, 410082, China

    Tao-Wen Liu

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  1. Tao-Wen Liu
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Correspondence to Tao-Wen Liu.

Additional information

This work was partially supported by the National Natural Science Foundation of China via grant 10671060.

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Liu, TW. A reduced Hessian SQP method for inequality constrained optimization. Comput Optim Appl 49, 31–59 (2011). https://doi.org/10.1007/s10589-009-9285-y

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  • DOI: https://doi.org/10.1007/s10589-009-9285-y

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