An interior point algorithm for semi-infinite linear programming
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
Interior point algorithms: theory and analysis
Interior point algorithms: theory and analysis
Relaxed cutting plane method for solving linear semi-infinite programming problems
Journal of Optimization Theory and Applications
HPOPT '96 Proceedings of the Stieltjes workshop on High performance optimization techniques
Computational Optimization and Applications
On Polyhedral Approximations of the Second-Order Cone
Mathematics of Operations Research
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 Optimization Approach for Radiosurgery Treatment Planning
SIAM Journal on Optimization
The Analytic Center Cutting Plane Method with Semidefinite Cuts
SIAM Journal on Optimization
The integration of an interior-point cutting plane method within a branch-and-price algorithm
Mathematical Programming: Series A and B
Mathematics of Operations Research
Cuts for mixed 0-1 conic 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 relaxed cutting plane method for semi-infinite semi-definite programming
Journal of Computational and Applied Mathematics
Efficient Production-Distribution System Design
Management Science
Journal of Global Optimization
An Analytic Center Cutting Plane Approach for Conic Programming
Mathematics of Operations Research
A Lifted Linear Programming Branch-and-Bound Algorithm for Mixed-Integer Conic Quadratic Programs
INFORMS Journal on Computing
A second-order cone cutting surface method: complexity and application
Computational Optimization and Applications
Conic mixed-integer rounding cuts
Mathematical Programming: Series A and B
FilMINT: An Outer Approximation-Based Solver for Convex Mixed-Integer Nonlinear Programs
INFORMS Journal on Computing
An algorithmic framework for convex mixed integer nonlinear programs
Discrete Optimization
Implementing the simplex method as a cutting-plane method, with a view to regularization
Computational Optimization and Applications
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We propose an interior point constraint generation (IPCG) algorithm for semi-infinite linear optimization (SILO) and prove that the algorithm converges to an ε-solution of SILO after a finite number of constraints is generated. We derive a complexity bound on the number of Newton steps needed to approach the updated μ-center after adding multiple violated constraints and a complexity bound on the total number of constraints that is required for the overall algorithm to converge. We implement our algorithm to solve the sector duration optimization problem arising in Leksell Gamma Knife® Perfexion™ (Elekta, Stockholm Sweden) treatment planning, a highly specialized treatment for brain tumors. Using real patient data provided by the Department of Radiation Oncology at Princess Margaret Hospital in Toronto, Ontario, Canada, we show that our algorithm can efficiently handle problems in real-life health-care applications by providing a quality treatment plan in a timely manner. Comparing our computational results with MOSEK, a commercial software package, we show that the IPCG algorithm outperforms the classical primal-dual interior point methods on sector duration optimization problem arising in Perfexion™ treatment planning. We also compare our results with that of a projected gradient method. In both cases we show that IPCG algorithm obtains a more accurate solution substantially faster.