Abstract
Bénasséni [Partial additive constant, J. Statist. Comput. Simul. 49 (1994), pp. 179–193] studied the partial additive constant problem in multidimensional scaling. This problem is quite challenging to solve, and Bénasséni proposed a numerical procedure for two special cases: the cross-set partial perturbation and the within-set partial perturbation. This paper casts the problem as a modern quadratic semi-definite programming (QSDP) problem, which is not only capable of dealing with general cases, but also enjoys a number of good properties. One of the good properties is that the proposed approach can find the minimal constant under very weak conditions. Another is that there exists a ready-to-use numerical package such as the QSDP solver in Toh [An inexact path-following algorithm for convex quadratic SDP, Math. Program. 112 (2008), pp. 221–254], allowing a great deal of flexibility in choosing the index set to which the partial constant should be added. Our numerical results show a significant improvement over that reported in Bénasséni (1994).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
