Strict Feasibility of Conic Optimization Problems

  • Hayato Waki
Part of the Mathematics for Industry book series (MFI, volume 5)


A conic optimization problem (COP) is the problem of minimizing a given linear objective function over the intersection of an affine space and a closed convex cone. Conic optimization problem is often used for solving nonconvex optimization problems. The strict feasibility of COP is important from the viewpoint of computation. The lack of the strict feasibility may cause the instability of computation. This article provides a brief introduction of COP and a characterization of the strict feasibility of COP. We also explain a facial reduction algorithm (FRA), which is based on the characterization. This algorithm can generate a strictly feasible COP which is equivalent to the original COP, or detect the infeasibility of COP.


Conic optimization problem Strong duality Strict feasibility Facial reduction 



The author was supported by a Grant-in-Aid for JSPS Fellow 20003236 and a Grant-in-Aid for Young Scientists (B) 22740056.


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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Institute of Mathematics for IndustryKyushu UniversityNishi-kuJapan

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