Radius of robust feasibility formulas for classes of convex programs with uncertain polynomial constraints

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• 作者：M.A. Goberna^a ; ^{mgoberna@ua.es" class="auth_mail" title="E-mail the corresponding author} ; V. Jeyakumar^b ; ^{v.jeyakumar@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author} ; G. Li^b ; ^{g.li@unsw.edu.au" class="auth_mail" title="E-mail the corresponding author} ; N. Linh^b ; ^{honglinh98t1@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Robust optimization ; Convex programming ; Data uncertainty ; Radius of robust feasibility
• 刊名：Operations Research Letters
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：44
• 期：1
• 页码：67-73
• 全文大小：404 K

文摘

The radius of robust feasibility of a convex program with uncertain constraints gives a value for the maximal ‘size’ of an uncertainty set under which robust feasibility can be guaranteed. This paper provides an upper bound for the radius for convex programs with uncertain convex polynomial constraints and exact formulas for convex programs with SOS-convex polynomial constraints (or convex quadratic constraints) under affine data uncertainty. These exact formulas allow the radius to be computed by commonly available software.