Bivalent quadratic optimization with sum-of-square of quadratic penalties

Tongli Zhang and Yong Xia ()
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Tongli Zhang: Nanjing Institute of Technology
Yong Xia: Beihang University

Journal of Combinatorial Optimization, 2025, vol. 50, issue 1, No 12, 17 pages

Abstract: Abstract The problem of maximizing the sum-of-square of quadratic functions with bivalent variables, denoted by (P), arises from bivalent quadratic optimization with K quadratic disjunctive penalties. Though NP-hard in general, (P) is polynomially solvable when the input matrices can concatenate to a fixed-rank matrix. We present a nonconvex quadratic semidefinite programming (SDP) relaxation, which provides a 0.4-approximate solution for (P). We show that the quadratic SDP relaxation can be approximately and globally solved to a precision $$\epsilon $$ via solving at most $$O((Kn^3/\epsilon )^{K/2})$$ linear SDP subproblems.

Keywords: Bivalent quadratic optimization; Quartic polynomial optimization; Approximation algorithm; Semidefinite programming (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-025-01339-7

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