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On modeling and global solutions for d.c. optimization problems by canonical duality theory

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  • Jin, Zhong
  • Y. Gao, David

Abstract

This paper presents a canonical d.c. (difference of canonical and convex functions) programming problem, which can be used to model general global optimization problems in complex systems. It shows that by using the canonical duality theory, a large class of nonconvex minimization problems can be equivalently converted to a unified concave maximization problem over a convex domain, which can be solved easily under certain conditions. Additionally, a detailed proof for triality theory is provided, which can be used to identify local extremal solutions. Applications are illustrated and open problems are presented.

Suggested Citation

  • Jin, Zhong & Y. Gao, David, 2017. "On modeling and global solutions for d.c. optimization problems by canonical duality theory," Applied Mathematics and Computation, Elsevier, vol. 296(C), pages 168-181.
    • Handle: RePEc:eee:apmaco:v:296:y:2017:i:c:p:168-181
    DOI: 10.1016/j.amc.2016.10.010
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    References listed on IDEAS

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    1. David Gao & Ning Ruan, 2010. "Solutions to quadratic minimization problems with box and integer constraints," Journal of Global Optimization, Springer, vol. 47(3), pages 463-484, July.
    2. Yi Chen & David Gao, 2016. "Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions," Journal of Global Optimization, Springer, vol. 64(3), pages 417-431, March.
    3. R. Horst & N. V. Thoai, 1999. "DC Programming: Overview," Journal of Optimization Theory and Applications, Springer, vol. 103(1), pages 1-43, October.
    4. Remigijus Paulavičius & Yaroslav Sergeyev & Dmitri Kvasov & Julius Žilinskas, 2014. "Globally-biased Disimpl algorithm for expensive global optimization," Journal of Global Optimization, Springer, vol. 59(2), pages 545-567, July.
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