Solving non-linear portfolio optimization problems with the primal-dual interior point method |
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Authors: | Jacek Gondzio Andreas Grothey |
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Institution: | School of Mathematics, The University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, United Kingdom |
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Abstract: | Stochastic programming is recognized as a powerful tool to help decision making under uncertainty in financial planning. The deterministic equivalent formulations of these stochastic programs have huge dimensions even for moderate numbers of assets, time stages and scenarios 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 ability to exploit their structure. Interior point methods are well-suited to the solution of very large non-linear 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 non-linear utility functions in the objective, can be solved with the state-of-the-art solver. |
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Keywords: | Portfolio optimization Nonlinear programming Interior point method Parallel computing |
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