Characterization of the optimum of a quadratic program with convex constraints. Application to sensor data fusion

We analyse theoretically a maximisation quadratic program which can arise in multi-target/multi-sensor area. The goal is to find the point x which minimizes the quadratic distance between x and a given point y. This optimum must lie in a convex constrained region defined by linear inequalities. We present a characterisation of this optimum in a compact dual form. This optimisation framework can be helpful, for example, in muti-objective programming like decentralized resource allocation.