## A decomposition method based on SQP for a class of multistage
nonlinear stochastic programs

### Xinwei Liu and Gongyun Zhao

Multi-stage stochastic programming problems arise in many practical
situations, such as production and manpower planning, portfolio
selections and so on. Generally, the size of the deterministic
equivalent of stochastic programs can be very large and not be
solvable directly by optimization approaches. Sequential quadratic
programming methods are iterative and very effective for solving
medium-size nonlinear programming. Based on scenario analysis, a
decomposition method based on SQP for solving a class of multistage
nonlinear stochastic programs is proposed, which generates the search
direction by solving parallelly a set of quadratic programming
subproblems with size much less than the original problem at each
iteration. Conjugate gradient methods can be introduced to derive the
estimates of the dual multiplier associated with the nonanticipativity
constraints. By selecting the step-size to reduce an exact penalty
function sufficiently, the algorithm terminates finitely at an
approximate optimal solution to the problem with any desirable
accuracy.
Research report, Department of Mathematics,
National University of Singapore, Singapore 119260

Contact: matliuxw@math.nus.edu.sg