Smooth optimization methods for minimax problems
SIAM Journal on Control and Optimization
Modified barrier functions (theory and methods)
Mathematical Programming: Series A and B
On the convergence of the exponential multiplier method for convex programming
Mathematical Programming: Series A and B
Nonlinear rescaling and proximal-like methods in convex optimization
Mathematical Programming: Series A and B
Asymptotic analysis for penalty and barrier methods in convex and linear programming
Mathematics of Operations Research
An Interior-Point Algorithm for Nonconvex Nonlinear Programming
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Interior Proximal and Multiplier Methods Based on Second Order Homogeneous Kernels
Mathematics of Operations Research
Penalty/Barrier Multiplier Methods for Convex Programming Problems
SIAM Journal on Optimization
Numerical Experiments with an Interior-Exterior Point Method for Nonlinear Programming
Computational Optimization and Applications
Primal-dual nonlinear rescaling method with dynamic scaling parameter update
Mathematical Programming: Series A and B
Cubic regularization of Newton method and its global performance
Mathematical Programming: Series A and B
Nonlinear Rescaling as Interior Quadratic Prox Method in Convex Optimization
Computational Optimization and Applications
On the local quadratic convergence of the primal-dual augmented Lagrangian method
Optimization Methods & Software
An entire space polynomial-time algorithm for linear programming
Journal of Global Optimization
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We introduce and study the primal-dual exterior point (PDEP) method for convex optimization problems. The PDEP is based on the non-linear rescaling (NR) multipliers method with dynamic scaling parameters update. The NR method at each step alternates finding the unconstrained minimizer of the Lagrangian for the equivalent problem with both Lagrange multipliers and scaling parameters vectors update. The NR step is replaced by solving the primal-dual (PD) system of equations. The application of the Newton method to the PD system leads to the PDEP method. We show that under the standard second-order optimality condition, the PDEP method generates a PD sequence, which globally converges to the PD solution with asymptotic quadratic rate.