Abstract

This paper analyzes the following robust optimization problem: min⁡{12x⊤Ax+a⊤x: α≤12x⊤Bx+b⊤x+c≤β, ∀ (B,b)∈B0},\smash{\min\Big\{\dfrac{1}{2}x^\top Ax+a^\top x:~\alpha\leq \dfrac{1}{2}x^\top Bx+b^\top x+c\leq\beta,~\forall~(B,b)\in{\mathcal B}_0\Big\}, } where B0≐{B1+μB2:μ∈[μ1,μ2]}×{b1+δb2:δ∈[δ1,δ2]}\mathcal{B}_0\doteq\{B_1+\mu B_2:\mu\in[\mu_1,\mu_2]\} \times\{b_1+\delta b_2:\delta\in[\delta_1,\delta_2]\}, with all the matrices involved are real symmetric, a,b∈Rna,b\in\mathbb{R}^n and α,β,δ1,δ2,μ1,μ2\alpha,\beta,\delta_1,\delta_2,\mu_1,\mu_2 are given real numbers. To be more precise, we establish characterizations of the fulfillment of: (i) the robust alternative result; (ii) the robust S-lemma, and (iii) the robust optimality, to the problem above. To that purpose, we apply the convexity result proved by one of the authors valid for nonhomogeneous quadratic functions, instead of the Dines convexity theorem.

Author information

Contact details are reproduced from the original publication and may be historical.

Ariel Pérez

Dep. de Ingeniería Matemática, Universidad de Concepción, Chile

arielperez@udec.cl

Keywords

  • Nonconvex quadratic programming under uncertainty
  • robust optimization
  • S-lemma
  • global optimality

Mathematics Subject Classification

90C20, 90C30, 90C26, 90C46

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Suggested citation

F. Flores-Bazán, A. Pérez. “Characterizing Optimality for a Class of Nonconvex Quadratic Robust Optimization Problems Bilaterally Quadratically Constrained Under Interval Uncertainty.” Journal of Convex Analysis 31 (2024), No. 1, 25–38. https://doi.org/10.68381/jca31002

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Published by Heldermann Verlag, 2024. Rights now held by Banach Press LLC.