A New Infeasible-Interior-Point Algorithm Based on Wide Neighborhoods for Symmetric Cone Programming

2016 ◽  
Vol 4 (2) ◽  
pp. 147-165 ◽  
Author(s):  
Chang-He Liu ◽  
Dan Wu ◽  
You-Lin Shang
Keyword(s):  
Interior Point ◽  
Symmetric Cone ◽  
Interior Point Algorithm ◽  
Cone Programming ◽  
Symmetric Cone Programming

scholarly journals An Arc Search Interior-Point Algorithm for Monotone Linear Complementarity Problems over Symmetric Cones

2018 ◽  
Vol 23 (1) ◽  
pp. 1-16
Author(s):  
Mohammad Pirhaji ◽  
Maryam Zangiabadi ◽  
Hossein Mansouri ◽  
Saman H. Amin
Keyword(s):  
Interior Point ◽  
Complementarity Problems ◽  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Symmetric Cone ◽  
Central Path ◽  
Interior Point Algorithm ◽  
Complexity Bound ◽  
Wide Neighborhood ◽  
Mathematical Problems

An arc search interior-point algorithm for monotone symmetric cone linear complementarity problem is presented. The algorithm estimates the central path by an ellipse and follows an ellipsoidal approximation of the central path to reach an "-approximate solution of the problem in a wide neighborhood of the central path. The convergence analysis of the algorithm is derived. Furthermore, we prove that the algorithm has the complexity bound O ( p rL) using Nesterov-Todd search direction and O (rL) by the xs and sx search directions. The obtained iteration complexities coincide with the best-known ones obtained by any proposed interior- point algorithm for this class of mathematical problems.

A long-step interior-point algorithm for symmetric cone Cartesian P*(κ)-HLCP

Optimization ◽  
2018 ◽  
Vol 67 (11) ◽  
pp. 2031-2060 ◽  
Author(s):  
S. Asadi ◽  
H. Mansouri ◽  
G. Lesaja ◽  
M. Zangiabadi
Keyword(s):  
Interior Point ◽  
Symmetric Cone ◽  
Interior Point Algorithm
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