Primal-dual interior-point methods
Primal-dual interior-point methods
Self-scaled barriers and interior-point methods for convex programming
Mathematics of Operations Research
Convergence of a Class of Inexact Interior-Point Algorithms for Linear Programs
Mathematics of Operations Research
Interior point algorithms for second-order cone problems with applications
Interior point algorithms for second-order cone problems with applications
A one-step smoothing Newton method for second-order cone programming
Journal of Computational and Applied Mathematics
A trust region SQP-filter method for nonlinear second-order cone programming
Computers & Mathematics with Applications
An alternating direction method for second-order conic programming
Computers and Operations Research
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Interior point methods (IPM) have been developed for all types of constrained optimization problems. In this work the extension of IPM to second order cone programming (SOCP) is studied based on the work of Andersen, Roos, and Terlaky. SOCP minimizes a linear objective function over the direct product of quadratic cones, rotated quadratic cones, and an affine set. It is described in detail how to convert several application problems to SOCP. Moreover, a proof is given of the existence of the step for the infeasible long-step path-following method. Furthermore, variants are developed of both long-step path-following and of predictor-corrector algorithms. Numerical results are presented and analyzed for those variants using test cases obtained from a number of application problems.