An unconstrained approach for solving low rank SDP relaxations of {-1, 1} quadratic problems

Authors

  • Luigi Grippo Dipartimento Informatica e Sistemistica "Antonio Ruberti"
  • Laura Palagi Dipartimento Informatica e Sistemistica "Antonio Ruberti"
  • Mauro Piacentini Dipartimento Informatica e Sistemistica "Antonio Ruberti"
  • Veronica Piccialli Dipartimento di Ingegneria dell'Impresa Universit√† di Tor Vergata

Keywords:

semidefinite programming, low rank factorization, boolean quadratic problem, nonlinear programming

Abstract

We consider low-rank semidefinite programming (LRSDP) relaxations of {-1, 1} quadratic problems that can be formulated as the nonconvex nonlinear programming problem of minimizing a quadratic function subject to separable quadratic equality constraints. We prove the equivalence of the LRSDP problem with the unconstrained minimization of a new merit function and we define an efficient and globally convergent algorithm for finding critical points of the LRSDP problem. Finally, we test our code on an extended set of instances of the Max-Cut problem and we report comparisons with other existing codes

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Published

14-12-2009

How to Cite

Grippo, L., Palagi, L., Piacentini, M., & Piccialli, V. (2009). An unconstrained approach for solving low rank SDP relaxations of {-1, 1} quadratic problems. Department of Computer and System Sciences Antonio Ruberti Technical Reports, 1(13). Retrieved from https://rosa.uniroma1.it/rosa00/index.php/dis_technical_reports/article/view/8856