The gradient descent procedure in [19] for user preference retrieval is based on linear additions of documents judged by the user. In contrast we design in this paper a multiplicative gradient descent search algorithm MG that uses a multiplicative query expansion strategy to adaptively improve the query vector. Our work generalizes the work in [19] in the following two aspects: various updating functions may be used in our algorithm; and multiplicative updating for a weight is dependent on the value of the corresponding index term, which is more realistic and applicable to real-valued vector space. The algorithm MG boosts the usefulness of an index term exponentially, while the algorithm in [19] does so linearly. We report a working prototype of the Web search project MAGRADS (Multiplicative Adaptive Gradient Descent Search) which is built upon algorithm MG, and its search performance analysis.