Solving combinatorial optimization problems using Karmakar's algorithm
Mathematical Programming: Series A and B
A cutting plane algorithm for convex programming that uses analytic centers
Mathematical Programming: Series A and B
Complexity analysis of the analytic center cutting plane method that uses multiple cuts
Mathematical Programming: Series A and B
Computational Optimization and Applications
Complexity Analysis of an Interior Cutting Plane Method for Convex Feasibility Problems
SIAM Journal on Optimization
A Multiple-Cut Analytic Center Cutting Plane Method for Semidefinite Feasibility Problems
SIAM Journal on Optimization
Multiple Cuts in the Analytic Center Cutting Plane Method
SIAM Journal on Optimization
An Analytic Center Based Column Generation Algorithm for Convex Quadratic Feasibility Problems
SIAM Journal on Optimization
The Analytic Center Quadratic Cut Method for Strongly Monotone Variational Inequality Problems
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
The Analytic Center Cutting Plane Method with Semidefinite Cuts
SIAM Journal on Optimization
An Analytic Center Cutting Plane Method for Semidefinite Feasibility Problems
Mathematics of Operations Research
Mathematics of Operations Research
Local Minima and Convergence in Low-Rank Semidefinite Programming
Mathematical Programming: Series A and B
A Semidefinite Programming Based Polyhedral Cut and Price Approach for the Maxcut Problem
Computational Optimization and Applications
A matrix generation approach for eigenvalue optimization
Mathematical Programming: Series A and B
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We present an analytic center cutting surface algorithm that uses mixed linear and multiple second-order cone cuts. Theoretical issues and applications of this technique are discussed. From the theoretical viewpoint, we derive two complexity results. We show that an approximate analytic center can be recovered after simultaneously adding p second-order cone cuts in O(plog驴(p+1)) Newton steps, and that the overall algorithm is polynomial. From the application viewpoint, we implement our algorithm on mixed linear-quadratic-semidefinite programming problems with bounded feasible region and report some computational results on randomly generated fully dense problems. We compare our CPU time with that of SDPLR, SDPT3, and SeDuMi and show that our algorithm outperforms these software packages on problems with fully dense coefficient matrices. We also show the performance of our algorithm on semidefinite relaxations of the maxcut and Lovasz theta problems.