This work develops an efficient decomposition algorithm for solving multipe
riod design problems (MPD) using interior point (JP) methods within a reduc
ed Hessian successive quadratic programming (rSQP) framework. MPD problems
often result when multiple planning scenarios or discretized uncertainty de
scriptions are incorporated in an optimization study. Each uncertain or pla
nning scenario is expressed as a separate period in MPD and all of these ar
e linked by a small set of design variables. The limiting factor in solving
MPD problems is a disproportionate increase in computational resources and
decrease in solution robustness, with an increase in the number of periods
. However, efficient decomposition strategies exist that exploit the block
bordered diagonal structure of these problems and provide a linear increase
in computational resources with the growth in periods. This was proposed i
n the (MPD-SQP) algorithm for general nonlinear MPD problems by Varvarezos,
Biegler and Grossmann, 1994. On the other hand, the MPD/SQP algorithm empl
oys an active set strategy for solving the quadratic programming (QP) sub-p
roblem and this is combinatorial in the number of active constraints. Also,
it needs to address a potentially different structure with each update of
the active set. This consideration usually leads MPD-SQP to adopt an early
termination for the QP problem, and this often requires additional SQP iter
ations. In order to solve the QP completely at each iteration, interior poi
nt methods have advantages as the number of updates is independent of the n
umber of active constraints and we deal with a fixed structure throughout t
he solution procedure. Incorporating these concepts leads to the MPD-rISQP
algorithm. The resulting algorithm maintains the nice features of the MPD-S
QP algorithm, such as a range and null space decomposition within each peri
od and a periodic problem decomposition. Moreover? the MPD-rISQP algorithm
proposed here employs a primal-dual path following interior point method to
address the QP. This permits a rigorous solution to the QP with an effort
that is linear with the number of periods and independent of the active set
. This algorithm is demonstrated on four example problems with up to 16000
variables. (C) 1999 Elsevier Science Ltd. All rights reserved.