An SQP algorithm for extended linear-quadratic problems in stochastic programming

Extended Linear-Quadratic Programming (ELQP) problems were introduced by Rockafellar and Wets for various models in stochastic programming and multistage optimization. Several numerical methods with linear convergence rates have been developed for solving fully quadratic ELQP problems, where the primal and dual coefficient matrices are positive definite. The authors present a two-stage sequential quadratic programming method for solving ELQP problems arising in stochastic programming. The first stage algorithm realizes global convergence and the second stage algorithm realizes superlinear local convergence under a condition called B-regularity. B-regularity is milder than the fully quadratic condition; the primal coefficient matrix need not be positive definite. Numerical tests are given to demonstrate the efficiency of the algorithm. Solution properties of the ELQP problem under B-regularity are also discussed.