Abstract
Motivated by problems associated with the emerging theory of distributionally robust Monte Carlo simulation, this paper addresses the classical equation Ax = b with n × n matrix A = A(θ) and n × 1 vector b = b(θ) depending on an m–tuple of parameters θ with components θi entering in a rank-one manner. For such a system, the following convexity problem is considered: Determine if the second partial derivative of a solution component xi(θ) with respect to a specified parameter θj is positive for all θ in a prescribed hypercube Θr of radius r ≥ 0. The main result of this paper is an extreme point solution of this problem. To this end, a factorization of the second derivative of xi(θ) is provided, which plays a major role in obtaining the so-called radius of convexity. Copyright © 2002 IFAC
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.
