AN ALGORITHM FOR QUADRATIC OPTIMIZATION WITH ONE QUADRATIC CONSTRAINTAND BOUNDS ON THE VARIABLES

This paper presents an efficient algorithm to solve a constrained opti mization problem with a quadratic object function, one quadratic const raint and (positivity) bounds on the variables. Against little computa tional cost, the algorithm allows for the inclusion of positivity of t he solution as prior knowledge. This is very useful for the solution o f those (linear) inverse problems where negative solutions are unphysi cal. The algorithm rewrites the solution as a function of the Lagrange multipliers, which is achieved with the help of the generalized eigen vectors, or equivalently, the generalized singular value decomposition . The next step is to find the Lagrange multipliers. The multiplier co rresponding to the quadratic constraint,which is known to be active, i s easy to find. The Lagrange multipliers corresponding to the positivi ty constraints are found with an iterative method that can be likened to the active set methods from quadratic programming.