A linear programming reformulation of the standard quadratic optimization problem

作者：de Klerk E^*; Pasechnik D V

来源：Journal of Global Optimization, 2007, 37(1): 75-84.

DOI：10.1007/s10898-006-9037-9

• linear programming
• standard quadratic optimization
• positive polynomials

The problem of minimizing a quadratic form over the standard simplex is known as the standard quadratic optimization problem (SQO). It is NP-hard, and contains the maximum stable set problem in graphs as a special case. In this note, we show that the SQO problem may be reformulated as an (exponentially sized) linear program (LP). This reformulation also suggests a hierarchy of polynomial-time solvable LP's whose optimal values converge finitely to the optimal value of the SQO problem. The hierarchies of LP relaxations from the literature do not share this finite convergence property for SQO, and we review the relevant counterexamples.

• 出版日期2007-1
• 单位南阳理工学院