Solvability And Primal-dual Partitions Of The Space Of Continuous Linear Semi-infinite Optimization Problems

2018 ◽  
Vol 22 (2) ◽  
Author(s):  
Abraham Barragán ◽  
Lidia Hernández ◽  
Maxim Todorov
Keyword(s):  
Optimization Problems ◽  
Continuous Linear ◽  
Primal Dual

Primal–Dual Mirror Descent Method for Constraint Stochastic Optimization Problems

2018 ◽  
Vol 58 (11) ◽  
pp. 1728-1736 ◽  
Author(s):  
A. S. Bayandina ◽  
A. V. Gasnikov ◽  
E. V. Gasnikova ◽  
S. V. Matsievskii
Keyword(s):  
Stochastic Optimization ◽  
Optimization Problems ◽  
Descent Method ◽  
Mirror Descent Method ◽  
Mirror Descent ◽  
Primal Dual

scholarly journals Random Matrix Approach for Primal-Dual Portfolio Optimization Problems

2017 ◽  
Vol 86 (12) ◽  
pp. 124804 ◽  
Author(s):  
Daichi Tada ◽  
Hisashi Yamamoto ◽  
Takashi Shinzato
Keyword(s):  
Portfolio Optimization ◽  
Random Matrix ◽  
Optimization Problems ◽  
Matrix Approach ◽  
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.

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