404. A higher-order extrapolation interior-point method for nonlinear optimization
Invited abstract in session WC-11: Interior point methods and applications - Part II, stream Interior point methods and applications.
Wednesday, 14:00-16:00Room: B100/5017
Authors (first author is the speaker)
| 1. | Pim Heeman
|
| Department of Mathematics, KTH Royal Institute of Technology | |
| 2. | Anders Forsgren
|
| Department of Mathematics, KTH Royal Institute of Technology |
Abstract
Interior-point methods for smooth optimization problems transform the problem into a problem without explicit inequalities by a logarithmic barrier transformation of the constraints. This gives an approximate problem where the accuracy of this approximation is controlled by a positive scalar, the so-called barrier parameter. The problem is solved for a sequence of decreasing barrier parameters, warm-starting the problem for the current parameter with the solution for the previous. A trade-off is here to be made between decreasing the barrier parameter fast enough to not solve too many optimization problems that have a fixed minimum cost associated with them on one hand and ensuring that the perturbed problem is not changed too drastically that warm-starting helps significantly on the other hand. In this talk, an accelerator for primal-dual interior-point methods following this scheme is proposed that uses higher-order derivatives, for asymptotic convergence at a rate proportional to the order of derivatives used. For problems of reduced complexity like convex quadratic programming problems, computational test results will be shown based on a proof-of-concept method using this accelerator.
Keywords
- Linear and nonlinear optimization
- Second- and higher-order optimization
Status: accepted
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