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An alternative multiplicative updates algorithm for nonnegative quadratic programming

In neural computation and statistical learning, there are many problems involving quadratic programming with nonnegativity constraints. In this paper, we study nonnegative quadratic programming (NQP) and develop an alternative multiplicative update algorithm for this problem by constructing new auxiliary functions. We prove that the new NQP algorithm can minimize the objective function gradually at each iteration. Similar to the well-known Fei Sha's multiplicative update NQP algorithm, the proposed one also has a simple close form and does not need to set any heuristics or other parameters that must be turned to ensure convergence. We illustrate the proposed multiplicative update NQP algorithm is comparable to Fei Sha's one in term of performance.