STABILITY OF LAGRANGIAN-DUALITY FOR NONCONVEX QUADRATIC-PROGRAMMING -SOLUTION METHODS AND APPLICATIONS IN COMPUTER VISION

The problem of minimizing a quadratic form over a ball centered at the origin is considered. The stability of Lagrangian duality is establis hed and complete characterizations of a global optimal solution are gi ven. On the basis of this theoretical study, two principal solution me thods are presented. An important application of nonconvex quadratic p rogramming is the computation of rite step to a new iterate in the Tru st Region (TR) approach methods which are known to be efficient for no nlinear optimization problems. Also, we discuss the mathematical model s of some important problems encountered in Computer Vision. Most of t hem can be formulated as a minimization of a sum of squares of nonline ar functions. A practical TR-based algorithm is proposed for nonlinear least squares problem which seems to be well suited for our applicati ons.