One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem.
A common problem with warmstarting for IPM is that an advanced starting point which is close to the boundary of the feasible region, as is typical, might lead to blocking of the search direction. A new "unblocking" strategy is suggested which attempts to directly address the issue of blocking by performing sensitivity analysis on the Newton step with the aim of increasing the size of the step that can be taken. This analysis is used in a new technique to warmstart interior point methods: we identify components of the starting point that are responsible for blocking and aim to improve these by using our sensitivity analysis.
Our method compares favourably with other warmstarting strategies on a selction of testproblems ranging from NETLIB to finding the efficient frontier of an asset liability management problem with 192 million variables. On average 50%-60% of iterations can be saved compared to a cold started IPM.
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