Polynomial convergence of two higher order interior-point methods for $$P_*(\kappa )$$ P ∗ ( κ ) -LCP in a wide neighborhood of the central path

2017 ◽  
Vol 76 (2) ◽  
pp. 243-264 ◽  
Author(s):  
Behrouz Kheirfam ◽  
Maryam Chitsaz
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Higher Order ◽  
Central Path ◽  
Wide Neighborhood

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.

Simplified analysis of a full Nesterov–Todd step infeasible interior-point method for symmetric optimization

2015 ◽  
Vol 08 (04) ◽  
pp. 1550071 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Point Method ◽  
Central Path ◽  
Complexity Bound ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Infeasible Interior Point Method ◽  
Simplified Analysis

We give a simplified analysis and an improved iteration bound of a full Nesterov–Todd (NT) step infeasible interior-point method for solving symmetric optimization. This method shares the features as, it (i) requires strictly feasible iterates on the central path of a perturbed problem, (ii) uses the feasibility steps to find strictly feasible iterates for the next perturbed problem, (iii) uses the centering steps to obtain a strictly feasible iterate close enough to the central path of the new perturbed problem, and (iv) reduces the size of the residual vectors with the same speed as the duality gap. Furthermore, the complexity bound coincides with the currently best-known iteration bound for full NT step infeasible interior-point methods.

Higher-Order Predictor-Corrector Interior Point Methods with Application to Quadratic Objectives

1993 ◽  
Vol 3 (4) ◽  
pp. 696-725 ◽  
Author(s):  
Tamra J. Carpenter ◽  
Irvin J. Lusting ◽  
John M. Mulvey ◽  
David F. Shanno
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Higher Order ◽  
Predictor Corrector

scholarly journals A FULL NT-STEP INFEASIBLE INTERIOR-POINT ALGORITHM FOR SEMIDEFINITE OPTIMIZATION BASED ON A SELF-REGULAR PROXIMITY

2011 ◽  
Vol 53 (1) ◽  
pp. 48-67 ◽  
Author(s):  
B. KHEIRFAM
Keyword(s):  
Interior Point ◽  
Interior Point Methods ◽  
Polynomial Complexity ◽  
Regular Function ◽  
Central Path ◽  
Semidefinite Optimization ◽  
Interior Point Algorithm ◽  
Iteration Bound

AbstractWe introduce a full NT-step infeasible interior-point algorithm for semidefinite optimization based on a self-regular function to provide the feasibility step and to measure proximity to the central path. The result of polynomial complexity coincides with the best known iteration bound for infeasible interior-point methods.

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