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DC Semidefinite programming and cone constrained DC optimization I: theory

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  • M. V. Dolgopolik

    (Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences)

Abstract

In this two-part study, we discuss possible extensions of the main ideas and methods of constrained DC optimization to the case of nonlinear semidefinite programming problems and more general nonlinear cone constrained optimization problems. In the first paper, we analyse two different approaches to the definition of DC matrix-valued functions (namely, order-theoretic and componentwise), study some properties of convex and DC matrix-valued mappings and demonstrate how to compute DC decompositions of some nonlinear semidefinite constraints appearing in applications. We also compute a DC decomposition of the maximal eigenvalue of a DC matrix-valued function. This DC decomposition can be used to reformulate DC semidefinite constraints as DC inequality constrains. Finally, we study local optimality conditions for general cone constrained DC optimization problems.

Suggested Citation

  • M. V. Dolgopolik, 2022. "DC Semidefinite programming and cone constrained DC optimization I: theory," Computational Optimization and Applications, Springer, vol. 82(3), pages 649-671, July.
    • Handle: RePEc:spr:coopap:v:82:y:2022:i:3:d:10.1007_s10589-022-00374-y
    DOI: 10.1007/s10589-022-00374-y
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    References listed on IDEAS

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    Cited by:

    1. M. V. Dolgopolik, 2023. "DC semidefinite programming and cone constrained DC optimization II: local search methods," Computational Optimization and Applications, Springer, vol. 85(3), pages 993-1031, July.

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