In this paper, we describe how to reformulate a problem that has second-order cone and/or semidefiniteness constraints in order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided.
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Received: March 10, 2001 / Accepted: January 18, 2002 Published online: September 27, 2002
Key Words. semidefinite programming – second-order cone programming – interior-point methods – nonlinear programming
Mathematics Subject Classification (2000): 20E28, 20G40, 20C20
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Benson, H., Vanderbei, R. Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming. Math. Program., Ser. B 95, 279–302 (2003). https://doi.org/10.1007/s10107-002-0350-x
- Nonlinear Programming
- Challenge Problem
- Nonlinear Program
- Related Constraint
- Implementation Challenge