Convergence Of Stabilized Sequential Quadratic Programming Methods For Piecewise Linear Quadratic Composite Optimization Problems

The classical sequential quadratic programming(SQP)method is mainly to solve a series of quadratic programming problems(SQP subproblems),so that the optimal solution of SQP subproblem converges to the optimal solution of the primal problem assuming the second order sufficient condition of the primal problem.As an important extension of SQP method,s SQP method has certain research value in solving ill-conditioned or degenerate constrained optimization problems.s SQP method adds a second penalty term on the basis of SQP subproblem,it is helpful to solve the degenerate constrained optimization problem where the Lagrange multiplier of the original solution is not unique.In this paper,we study the convergence and the convergence rate of the stabilized sequential quadratic programming(s SQP)method of convex piecewise linear quadratic composite optimization problems assuming the second order sufficient condition of the composite optimization problem.The difficulties of this paper lie in the equivalent characterization of KKT system and affine variational inequality,solvability of subproblems,etc.