Solving Two-Trust-Region Subproblems Using Semidefinite Optimization with Eigenvector Branching

Kurt M. Anstreicher ()
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Kurt M. Anstreicher: University of Iowa

Journal of Optimization Theory and Applications, 2024, vol. 202, issue 1, No 14, 303-319

Abstract: Abstract Semidefinite programming (SDP) problems typically utilize a constraint of the form $$X\succeq xx^T$$ X ⪰ x x T to obtain a convex relaxation of the condition $$X=xx^T$$ X = x x T , where $$x\in \mathbb {R}^n$$ x ∈ R n . In this paper, we consider a new hyperplane branching method for SDP based on using an eigenvector of $$X-xx^T$$ X - x x T . This branching technique is related to previous work of Saxeena et al. (Math Prog Ser B 124:383–411, 2010, https://doi.org/10.1007/s10107-010-0371-9 ) who used such an eigenvector to derive a disjunctive cut. We obtain excellent computational results applying the new branching technique to difficult instances of the two-trust-region subproblem.

Keywords: Semidefinite programming; Semidefinite optimization; Conic optimization; Nonconvex quadratic programming; Trust region subproblem; 90C20; 90C22; 90C26 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10957-022-02064-5

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