TY - JOUR
T1 - Robust solutions for a class of quadratic optimization problems without classical convexity assumptions
AU - Flores-Bazán, F.
AU - García, Y.
AU - Pérez, A.
N1 - Publisher Copyright:
© 2024 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2024/4/2
Y1 - 2024/4/2
N2 - We investigate a class of quadratic robust optimization problems under lower and upper bounds on the constraint, and establish, a robust alternative-type result and a robust S-lemma, provided a generalized convexity assumption and a suitable Slater's condition hold. The robust S-lemma allows us to characterize the robust solutions via first and second order optimality conditions. Relationships with strong duality are also proposed. We base our analysis on Dines' theorem concerning the convexity of images of two quadratic forms, and therefore the homogenization procedure plays a fundamental role. Additionally, we present a novel convex image result suitable for situations where existing results elsewhere are not applicable. This is illustrated by a concrete example.
AB - We investigate a class of quadratic robust optimization problems under lower and upper bounds on the constraint, and establish, a robust alternative-type result and a robust S-lemma, provided a generalized convexity assumption and a suitable Slater's condition hold. The robust S-lemma allows us to characterize the robust solutions via first and second order optimality conditions. Relationships with strong duality are also proposed. We base our analysis on Dines' theorem concerning the convexity of images of two quadratic forms, and therefore the homogenization procedure plays a fundamental role. Additionally, we present a novel convex image result suitable for situations where existing results elsewhere are not applicable. This is illustrated by a concrete example.
KW - convex image
KW - global optimality
KW - Nonconvex quadratic programming under uncertainty
KW - robust optimization
KW - S-lemma
KW - Programación cuadrática no convexa bajo incertidumbre
KW - Optimización robusta
KW - S-lemma
KW - Optimalidad global
KW - Imagen convexa
UR - http://www.scopus.com/inward/record.url?scp=85189158505&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/8db95ccc-9c37-32f1-87fa-8c2214ef19d9/
U2 - 10.1080/02331934.2024.2335948
DO - 10.1080/02331934.2024.2335948
M3 - Article in a journal
AN - SCOPUS:85189158505
SN - 0233-1934
JO - Optimization
JF - Optimization
ER -