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

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  • Kurt M. Anstreicher

    (University of Iowa)

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.

Suggested Citation

  • Kurt M. Anstreicher, 2024. "Solving Two-Trust-Region Subproblems Using Semidefinite Optimization with Eigenvector Branching," Journal of Optimization Theory and Applications, Springer, vol. 202(1), pages 303-319, July.
    • Handle: RePEc:spr:joptap:v:202:y:2024:i:1:d:10.1007_s10957-022-02064-5
    DOI: 10.1007/s10957-022-02064-5
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