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

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.

scholarly journals A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization

2021 ◽  
Author(s):  
Joachim Dahl ◽  
Erling D. Andersen
Keyword(s):  
Interior Point ◽  
Significant Contribution ◽  
Symmetric Cone ◽  
Conic Optimization ◽  
Interior Point Algorithm ◽  
Quadratic Cone ◽  
3 Dimensional ◽  
Primal Dual ◽  
Practical Algorithm ◽  
Numerical Performance

AbstractA new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It is a generalization of the famous algorithm suggested by Nesterov and Todd for the symmetric conic case, and uses primal-dual scalings for nonsymmetric cones proposed by Tunçel. We specialize Tunçel’s primal-dual scalings for the important case of 3 dimensional exponential-cones, resulting in a practical algorithm with good numerical performance, on level with standard symmetric cone (e.g., quadratic cone) algorithms. A significant contribution of the paper is a novel higher-order search direction, similar in spirit to a Mehrotra corrector for symmetric cone algorithms. To a large extent, the efficiency of our proposed algorithm can be attributed to this new corrector.

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