The Adaptive-lasso With Linear Constraints

The lasso is more widely used after least angle regression proposed by Bradley Efron et al,later Zou proposed adaptive-lasso based lasso,which makes different shrinkage to every parameter and also has oracle properties in theory.So this article considers some special situation that prior parameter conditions can be known expect for the sample data information,it will be improved if we can use parameter constraints of prior conditions to estimate model parameters and do variable selection reasonably,so I added linear constraints to the Adaptive-lasso proposed by Zou,linear constraints conditions basically covers most of prior information in real life,so Adaptive-lasso with linear constraints makes variable selection more extensive.In chapter 3,we give the definition of Adaptive-lasso with linear constraints and Lagrange form of primal problem by Lagrange multiplier,and discuss the dual problem of primal problem,later we infer an explicit expression for the primal solution (?) and the fitted response (?) by KKT condition,also get the relationship between the primal solution(?) and the dual solution (?),(?),(?).At last,we give the coordinate descent algorithm of this problem we discussed,and then tested Adaptive-lasso with linear constraints have less parameter estimation error than primal Adaptive-lasso in certain cases by the algorithm,it is improved.