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

Tran Nghi () and Nguyen Nang Tam ()
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Tran Nghi: Hanoi Pedagogical University 2
Nguyen Nang Tam: Hanoi Pedagogical University 2

Journal of Optimization Theory and Applications, 2020, vol. 187, issue 2, No 9, 448-468

Abstract: 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.

Keywords: Cubic program; Solution existence; Frank–Wolfe theorem; Quadratic variational inequality; Solvability; 90C30; 90C31 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s10957-020-01759-x

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