Primal-Dual Algorithms for Linear Optimization Based on Self-Regular Proximities

2018 ◽  
pp. 47-66
Keyword(s):  
Linear Optimization ◽  
Primal Dual

AN INTERIOR POINT APPROACH FOR SEMIDEFINITE OPTIMIZATION USING NEW PROXIMITY FUNCTIONS

2009 ◽  
Vol 26 (03) ◽  
pp. 365-382 ◽  
Author(s):  
M. REZA PEYGHAMI
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Linear Optimization ◽  
Kernel Functions ◽  
Semidefinite Optimization ◽  
Special Choice ◽  
Simple Analysis ◽  
New Class ◽  
Iteration Bound ◽  
Primal Dual

Kernel functions play an important role in interior point methods (IPMs) for solving linear optimization (LO) problems to define a new search direction. In this paper, we consider primal-dual algorithms for solving Semidefinite Optimization (SDO) problems based on a new class of kernel functions defined on the positive definite cone [Formula: see text]. Using some appealing and mild conditions of the new class, we prove with simple analysis that the new class-based large-update primal-dual IPMs enjoy an [Formula: see text] iteration bound to solve SDO problems with special choice of the parameters of the new class.

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.

scholarly journals Primal-dual stability in continuous linear optimization

2007 ◽  
Vol 116 (1-2) ◽  
pp. 129-146 ◽  
Author(s):  
Miguel A. Goberna ◽  
Maxim I. Todorov
Keyword(s):  
Linear Optimization ◽  
Continuous Linear ◽  
Primal Dual

scholarly journals Primal, dual and primal-dual partitions in continuous linear optimization

Optimization ◽  
2007 ◽  
Vol 56 (5-6) ◽  
pp. 617-628 ◽  
Author(s):  
M. A. Goberna ◽  
M. I. Todorov§
Keyword(s):  
Linear Optimization ◽  
Continuous Linear ◽  
Primal Dual

An adaptive-step primal-dual interior point algorithm for linear optimization

2009 ◽  
Vol 71 (12) ◽  
pp. e2305-e2315
Author(s):  
Min Kyung Kim ◽  
Yong-Hoon Lee ◽  
Gyeong-Mi Cho
Keyword(s):  
Interior Point ◽  
Linear Optimization ◽  
Interior Point Algorithm ◽  
Primal Dual ◽  
Adaptive Step
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