The four-minimizer bound for homogeneous QCQPs with two constraints

Consider the homogeneous quadratically constrained quadratic optimization problem denoted by

.Astrictlocalnonglobalminimizerisafeasiblepointthatisastrictlocalminimizerbutnotaglobalminimizer.Fourminimizerbound.Theproblem. A strict local non-global minimizer is a feasible point that is a strict local minimizer but not a global minimizer. **Four-minimizer bound.** The problem

has at most four strict local non-global minimizers. The statement is presented after an example exhibiting four such minimizers, so the bound is sharp within the paper's discussion; its general validity is not established by the supplied text.

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Primary source

Mengmeng Song, Hongying Liu and Yong Xia, “On Local Minimizers of Quadratically Constrained Nonconvex Homogeneous Quadratic Optimization with at Most Two Constraints”, arXiv:2107.05816 (2021).

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