Optimality theorems for robust least squares problems
Optimization Eruditorum, Volume 3, Issue 1, April 2026, Pages 1–6
MOON HEE KIM
College of General Education, Tongmyong University, Busan 48520, Korea
GWI SOO KIM
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
GUE MYUNG LEE
Department of Applied Mathematics, Pukyong National University, Busan 48513, Korea
JEN-CHIH YAO
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
Abstract
We consider a robust least square (RLS) problem, which is the robust counterpart of the least squares problem. The uncertainty set for the RLS problem is a compact and convex set. We give optimality theorems for the RLS problem by using the dual approach. We calculate the conjugate function of certain form of distance function. We get an optimality theorem for the RLS problem, which is expressed with the orthogonal spaces of the null spaces and the pseudoinverses of matrices in the uncertainty set.
Cite this Article as
Moon Hee Kim, Gwi Soo Kim, Gue Myung Lee, Jen-Chih Yao, Optimality theorems for robust least squares problems, Optimization Eruditorum, 3(1), 1–6, 2026