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A penalty derivative-free algorithm for nonlinear constrained optimization

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Abstract

In this paper, we modify a derivative-free line search algorithm (DFL) proposed in the Ref. (Liuzzi et al. SIAM J Optimiz 20(5):2614–2635, 2010) to minimize a continuously differentiable function of box constrained variables or unconstrained variables with nonlinear constraints. The first-order derivatives of the objective function and of the constraints are assumed to be neither calculated nor explicitly approximated. Different line-searches are used for box-constrained variables and unconstrained variables. Accordingly the convergence to stationary points is proved. The computational behavior of the method has been evaluated on a set of test problems. The performance and data profiles are used to compare with DFL.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant No. 11101262,11171050,U1232112, Dalian University of Technology Special Fund under Grant No. DUTTX2011106, Key Disciplines of Shanghai Municipality under Grant No. S30104, and a Grant of ’The First-class Discipline of Universities in Shanghai’.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Wei Lv, Qiang Sun & Ruirui Sui

  2. Department of Materials and Energy Research, Shanghai Institute of Applied Physics Chinese Academy of Sciences, Shanghai, 201204, China

    He Lin

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  1. Wei Lv
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  2. Qiang Sun
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  3. He Lin
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  4. Ruirui Sui
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Correspondence to Wei Lv.

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Lv, W., Sun, Q., Lin, H. et al. A penalty derivative-free algorithm for nonlinear constrained optimization. Optim Lett 9, 1213–1229 (2015). https://doi.org/10.1007/s11590-014-0832-9

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  • DOI: https://doi.org/10.1007/s11590-014-0832-9

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