Smoothing Newton Methods For Sloving E₁ Norm Optimization Model

Usually,we use the feature of object to compose a high dimensional vector to represent the object.The similarity between objects is usually characterized by the distance of two vectors. Extended to linear norm space, the distance can be described by l1norm optimization model. Such as in face recognition system,human feature can be used to constitute a high dimensional vector,l1norm optimization model should be solved to recognized human face. Therefore,l1 norm optimization model become very important.This paper is devoted to a kind of 11 norm optimization problem with linear constraints. We smooth the objective function and reformulate such problems as second-order cone constraint optimizations by introducing second order cone constraints. The dual problem is constructed and solved to reduce the computation cost by the duality theory. The KKT system of the dual problem is converted into a system of nonsmooth equations based on the Fischer-Burmeister function and a smoothing newton method with Armijo line search is used to solve this nonsmooth system. We verify the nonsingularity of JΦand obtain that the algorithm has global and local quadratic convergence. Numerical experiments running on Matlab are reported at the end of the thesis.