Abstract. This paper presents an algorithm for solving multi-stage stochastic nonlinear programs. The algorithm is based on the Lagrangian dual method which relaxes the nonanticipativity constraints, and the barrier function method which enhances the smoothness of the dual objective function so that the Newton search directions can be used. The algorithm is shown to be of globally linear convergence and of polynomial-time complexity. Keywords: Multi-stage stochastic nonlinear programming, Lagrangian dual, Self-concordant
|
406
|
Nonlinear Programming. Theory and Algorithms
– Bazaraa, Sherali, et al.
- 1993
|
|
195
|
Interior-point polynomial algorithms in convex programming
– Nesterov, Nemirovskii
- 1994
|
|
69
|
L-shaped linear programs with applications to optimal control and stochastic programming
– SLYKE, WETS
- 1969
|
|
41
|
a computer code for the multistage stochastic linear programming problem
– MSLIP
- 1990
|
|
27
|
Stochastic Decomposition: A Statistical Method for Large Scale Stochastic Linear Programming
– Higle, Sen
- 1996
|
|
27
|
Interior-point methods for convex programming
– Jarre
- 1995
|
|
24
|
An augmented Lagrangian decomposition method for block diagonal linear programming problems
– Ruszczy'nski
- 1995
|
|
23
|
A scenario approach to capacity planning
– Eppen, Martin, et al.
- 1989
|
|
21
|
A Successive Linear Approximation Procedure for Stochastic, Dynamic Vehicle Allocation Problems
– Frantzekakis, Powell
- 1990
|
|
21
|
Applying the progressive hedging algorithm to stochastic generalized networks
– Mulvey, Vladimirou
- 1991
|
|
16
|
Multi-stage stochastic optimization applied to energy planning
– Pereira, Pinto
- 1991
|
|
14
|
and François Louveaux. Introduction to stochastic programming
– Birge
- 1997
|
|
11
|
A sucient condition for selfconcordance with application to some classes of structured convex programming problems
– Hertog, Jarre, et al.
- 1995
|
|
10
|
Stochastic programming problems: Examples from the literature
– King
- 1988
|
|
9
|
Interior-point methods with decomposition for solving large-scale linear programs
– Zhao
- 1999
|
|
8
|
Current trends in stochastic programming computation and applications
– Birge
- 1995
|
|
8
|
The allocation of aircraft to routes - an example of linear programming under uncertain demand
– Ferguson, Dantzig
- 1956
|
|
8
|
Approximate scenario solutions in the progressive hedging algorithm
– Helgason, Wallace
- 1991
|
|
8
|
Horizontal and vertical decomposition in interior point methods for linear programs," Working paper
– Kojima, Megiddo, et al.
- 1993
|
|
8
|
A log-barrier method with Benders decomposition for solving two-stage stochastic programs
– Zhao
- 1997
|
|
7
|
The Russel- Yasuda Kasai Model: An asset/liability model for a Japanese insurance company using multistage stochastic programming," Interfaces 24
– Carino, Kent, et al.
- 1994
|
|
5
|
Modelling investment uncertainty in the costs of global CO 2 emission policy
– Birge, Rosa
- 1995
|
|
4
|
Stochastic programming in production planning: a case with non-simple recourse, Statistica Neerlandica 31
– Peters, Boskma, et al.
- 1977
|
|
4
|
Wets, "Scenarios and policy aggregation in optimization under uncertainty
– Rockafellar, J-B
- 1991
|
|
3
|
A standard input format for multistage stochastic linear programs
– Birge, Dempster, et al.
- 1987
|
|
2
|
and A Ruszczy'nski, "A new scenario decomposition method for large scale stochastic optimization
– Mulvey
- 1995
|
|
1
|
Scenario analysis vis bundle decomposition
– Chen, Robinson
- 1995
|
|
1
|
On implementation of a Lagrangian dual method for solving multi-stage stochastic programming problems
– Liu, Toh, et al.
- 2000
|
|
1
|
Birge abd F. Louveaux, Introduction to Stochastic Programming
– R
- 1997
|
|
