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On duality theory for non-convex semidefinite programming

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Abstract

In this paper, with the help of convex-like function, we discuss the duality theory for nonconvex semidefinite programming. Our contributions are: duality theory for the general nonconvex semidefinite programming when Slater’s condition holds; perfect duality for a special case of the nonconvex semidefinite programming for which Slater’s condition fails. We point out that the results of Fan (Appl. Math. Lett. 18:1068–1073, 2005) can be regarded as a special case of our result.

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Authors and Affiliations

  1. School of Mathematical Sciences, Jiangsu Key Laboratory for NSLSCS, Nanjing Normal University, Nanjing, 210046, China

    Wenyu Sun & Chengjin Li

  2. School of Mathematics and Computer Science, Fujian Normal University, Fuzhou, 350007, China

    Chengjin Li

  3. Graduate Program in Production and Systems Engineering (PPGEPS), Pontifical Catholic University of Panara (PUCPR), 81611-970, Curitiba, Parana, Brazil

    Raimundo J. B. Sampaio

Authors
  1. Wenyu Sun
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  2. Chengjin Li
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  3. Raimundo J. B. Sampaio
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Correspondence to Wenyu Sun.

Additional information

This work was supported by National Natural Science Foundation of China (grant No. 10871098, No. 11071122), the Natural Science Fund of Jiangsu Province (grant No. BK2009397), and CNPq of Brazil.

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Sun, W., Li, C. & Sampaio, R.J.B. On duality theory for non-convex semidefinite programming. Ann Oper Res 186, 331–343 (2011). https://doi.org/10.1007/s10479-011-0861-z

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