Complexity bounds for primal-dual methods minimizing the model of objective function

2017 ◽  
Vol 171 (1-2) ◽  
pp. 311-330 ◽  
Author(s):  
Yu. Nesterov
Keyword(s):  
Objective Function ◽  
Complexity Bounds ◽  
Dual Methods ◽  
Primal Dual

Primal-Dual Methods for Solving Infinite-Dimensional Games

2015 ◽  
Vol 166 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Pavel Dvurechensky ◽  
Yurii Nesterov ◽  
Vladimir Spokoiny
Keyword(s):  
Infinite Dimensional ◽  
Dual Methods ◽  
Primal Dual

scholarly journals A New Homotopy Proximal Variable-Metric Framework for Composite Convex Minimization

2021 ◽  
Author(s):  
Quoc Tran-Dinh ◽  
Ling Liang ◽  
Kim-Chuan Toh
Keyword(s):  
Convergence Rates ◽  
Optimization Problems ◽  
Linear Convergence ◽  
Convex Minimization ◽  
Variable Metric ◽  
Complexity Bounds ◽  
Convex Problems ◽  
Convex Minimization Problems ◽  
Global Iteration ◽  
Primal Dual

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is to utilize a new parameterization strategy of the optimality condition to design a class of homotopy proximal variable-metric algorithms that can achieve linear convergence and finite global iteration-complexity bounds. We identify at least three subclasses of convex problems in which our approach can apply to achieve linear convergence rates. The second idea is a new primal-dual-primal framework for implementing proximal Newton methods that has attractive computational features for a subclass of nonsmooth composite convex minimization problems. We specialize the proposed algorithm to solve a covariance estimation problem in order to demonstrate its computational advantages. Numerical experiments on the four concrete applications are given to illustrate the theoretical and computational advances of the new methods compared with other state-of-the-art algorithms.

scholarly journals An interior point algorithm for solving linear optimization problems using a new trigonometric kernel function

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1471-1486
Author(s):  
S. Fathi-Hafshejani ◽  
Reza Peyghami
Keyword(s):  
Kernel Function ◽  
Interior Point ◽  
Optimization Problems ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Worst Case ◽  
Complexity Bounds ◽  
Linear Optimization Problems ◽  
Primal Dual ◽  
The Given

In this paper, a primal-dual interior point algorithm for solving linear optimization problems based on a new kernel function with a trigonometric barrier term which is not only used for determining the search directions but also for measuring the distance between the given iterate and the ?-center for the algorithm is proposed. Using some simple analysis tools and prove that our algorithm based on the new proposed trigonometric kernel function meets O (?n log n log n/?) and O (?n log n/?) as the worst case complexity bounds for large and small-update methods. Finally, some numerical results of performing our algorithm are presented.

Primal–Dual Methods

2021 ◽  
pp. 525-558
Author(s):  
David G. Luenberger ◽  
Yinyu Ye
Keyword(s):  
Dual Methods ◽  
Primal Dual
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