文档介绍：Solving Nonlinear Portfolio Optimization Problems
with the Primal-Dual Interior Point Method
Jacek Gondzio Andreas Grothey
April 2, 2004
MS-04-001
For other papers in this series see .uk/preprints
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Solving Nonlinear Portfolio Optimization Problems with the
Primal-Dual Interior Point Method∗
Jacek Gondzio† Andreas Grothey‡
School of Mathematics
The University of Edinburgh
Mayfield Road, Edinburgh EH9 3JZ
United Kingdom.
March 31st, 2004
∗Supported by the Engineering and Physical Sciences Research Council of UK, EPSRC grant GR/R99683/01.
†Email: J.******@, URL: /~gondzio/
‡Email: A.******@, URL: /~agr/
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Solving Nonlinear Portfolio Optimization Problems with the Primal-Dual
Interior Point Method
Abstract
Stochastic programming is recognized as a powerful tool to help decision making under un-
certainty in financial planning. The deterministic equivalent formulations of these stochastic
programs have huge dimensions even for moderate numbers of assets, time stages and sce-
narios per time stage. So far models treated by mathematical programming approaches have
been limited to simple linear or quadratic models due to the inability of currently available
solvers to solve NLP problems of typical sizes. However stochastic programming problems
are highly structured. The key to the efficient solution of such problems is therefore the abil-
ity to exploit their structure. Interior point methods are well-suited to the solution of very
large nonlinear optimization problems. In this paper we exploit this feature and show how
portfolio optimization problems with sizes measured in millions of constraints and decision
variables, featuring constraints on semi-variance, skewness or nonlinear utility functions in
the objective, can be solved with the state-of-the-art solver.
1 Introduction
Stochastic programming is recognized as an important tool in financial planning.