TY - JOUR
ID - 13631
TI - Primal-dual path-following algorithms for circular programming
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Alzalg, Baha
AU - Pirhaji, Mohammad
AD - The University of Jordan
AD - Shahrekord University
Y1 - 2017
PY - 2017
VL - 2
IS - 2
SP - 65
EP - 85
KW - Circular cone programming
KW - Interior point methods
KW - Euclidean Jordan algebra
KW - Self-concordance
DO - 10.22049/cco.2017.25865.1051
N2 - Circular programming problems are a new class of convex optimization problems that include second-order cone programming problems as a special case. Alizadeh and Goldfarb [Math. Program. Ser. A 95 (2003) 3-51] introduced primal-dual path-following algorithms for solving second-order cone programming problems. In this paper, we generalize their work by using the machinery of Euclidean Jordan algebras associated with the circular cones to derive primal-dual path-following interior point algorithms for circular programming problems. We prove polynomial convergence of the proposed algorithms by showing that the circular logarithmic barrier is a strongly self-concordant barrier. The numerical examples show the path-following algorithms are simple and efficient.
UR - http://comb-opt.azaruniv.ac.ir/article_13631.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13631_3b92d66c63867691344b503a2f0746f7.pdf
ER -