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Outer Approximation Algorithm for One Class of Convex Mixed-Integer Nonlinear Programming Problems with Partial Differentiability

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Abstract

In this paper, we mainly study one convex mixed-integer nonlinear programming problem with partial differentiability and establish one outer approximation algorithm for solving this problem. With the help of subgradients, we use the outer approximation method to reformulate this convex problem as one equivalent mixed-integer linear program and construct an algorithm for finding optimal solutions. The result on finite steps convergence of the algorithm is also presented.

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Acknowledgments

The authors are grateful to the referee for careful reading this paper and valuable comments which help us to improve the original version. This research was supported by the National Natural Science Foundations of P. R. China (Grant Nos. 11401518 and 11261067) and the IRTSTYN, and by the Claude Leon Foundation of South Africa.

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Authors and Affiliations

  1. Department of Mathematics, Yunnan University, Kunming, 650091, People’s Republic of China

    Zhou Wei

  2. School of Computational and Applied Mathematics, University of the Witwatersrand, Wits, Johannesburg, 2050, South Africa

    Zhou Wei & M. Montaz Ali

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  1. Zhou Wei
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  2. M. Montaz Ali
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Correspondence to M. Montaz Ali.

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Wei, Z., Ali, M.M. Outer Approximation Algorithm for One Class of Convex Mixed-Integer Nonlinear Programming Problems with Partial Differentiability. J Optim Theory Appl 167, 644–652 (2015). https://doi.org/10.1007/s10957-015-0715-y

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  • DOI: https://doi.org/10.1007/s10957-015-0715-y

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