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A Frank–Wolfe-Type Theorem for Cubic Programs and Solvability for Quadratic Variational Inequalities

Author

Listed:
  • Tran Nghi

    (Hanoi Pedagogical University 2)

  • Nguyen Nang Tam

    (Hanoi Pedagogical University 2)

Abstract

In this paper, we present a Frank–Wolfe-type theorem for nonconvex cubic programming problems. This result is a direct extension of the previous ones by Andronov et al. (Izvestija Akadem. Nauk SSSR, Tekhnicheskaja Kibernetika 4:194–197, 1982) and Flores-Bazán et al. (Math. Program. 145:263–290, 2014). Under suitable conditions, we characterize the compactness of the solution set of cubic programming problems. Sufficient conditions for the existence of solutions of quadratic variational inequalities are proposed. We also provide several numerical examples, which not only illustrate the obtained results but also show that the existing results cannot apply.

Suggested Citation

  • Tran Nghi & Nguyen Nang Tam, 2020. "A Frank–Wolfe-Type Theorem for Cubic Programs and Solvability for Quadratic Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 187(2), pages 448-468, November.
    • Handle: RePEc:spr:joptap:v:187:y:2020:i:2:d:10.1007_s10957-020-01759-x
    DOI: 10.1007/s10957-020-01759-x
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    References listed on IDEAS

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    6. B. Curtis Eaves, 1971. "On Quadratic Programming," Management Science, INFORMS, vol. 17(11), pages 698-711, July.
    7. Luo, Z-Q. & Zhang, S., 1997. "On the extensions of the Frank-Worfe theorem," Econometric Institute Research Papers EI 9748/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
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