Large-scale Extended Linear-quadratic Programming and Multistage Optimization

Optimization problems in discrete time can be modeled more flexibly by extended linearquadratic programming than by traditional linear or quadratic programming, because penalties and other expressions that may substitute for constraints can readily be incorporated and dualized. At the same time, dynamics can be written with state vectors as in dynamic programming and optimal control. This suggests new primal-dual approaches to solving multistage problems. The special setting for such numerical methods is described. New results are presented on the calculation of gradients of the primal and dual objective functions and on the convergence effects of strict quadratic regularization. ∗ Dept. of Mathematics, University of Washington GN-50, Seattle, WA 98195. This work was supported by AFOSR grant 89-0081 and NSF grant DMS 881-9586.