Abstract
An improved algorithm is proposed for the minimization of a quadratic function in zero-one variables under quadratic constraints which is based on the idea of additive penalties proposed by P. Hansen. At first, the quadratic function in which all the coefficients except the constant term are nonnegative is obtained by the introduction of the negative variables, and the constant term is a tighter bound of the function. Starting from the tighter bound, some properties are obtained and some efficient tests are established. To obtain a much tighter bound, a simple heuristic method is suggested instead of solving a linear programming problem. Furthermore, the flexibility dealing with some tests is discussed and it is also helpful to the algorithm.
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