Approximation algorithms for indefinite quadratic programming. (English) Zbl 0845.90095

The author considers the nonconvex quadratic programming problem: \[ \text{Minimize}\quad \textstyle{{1\over 2}} (x^{\mathbb T} Hx)+ h^{\mathbb T} x\quad\text{subject to } Wx\geq b. \] An algorithm for finding an \(\varepsilon\)-approximation solution of this problem is suggested. The algorithm is polynomial in \(1/\varepsilon\) for fixed \(t\), where \(t\) is the number of negative eigenvalues of the quadratic term. The algorithm is exponential in \(t\) for fixed \(\varepsilon\). The results are applied to a special case of the quadratic knapsack problem. It is shown that there exists an approximation algorithm for this problem which is polynomial in \(t\).


90C20 Quadratic programming
90-08 Computational methods for problems pertaining to operations research and mathematical programming
90C26 Nonconvex programming, global optimization
Full Text: DOI


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