TY - GEN
T1 - Generalized affine scaling trajectory analysis for linearly constrained convex programming
AU - Qian, Xun
AU - LIAO, Lizhi
N1 - Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.
PY - 2018
Y1 - 2018
N2 - In this paper, we propose and analyze a continuous trajectory, which is the solution of an ordinary differential equation (ODE) system for solving linearly constrained convex programming. The ODE system is formulated based on a first-order interior point method in [Math. Program., 127, 399–424 (2011)] which combines and extends a first-order affine scaling method and the replicator dynamics method for quadratic programming. The solution of the corresponding ODE system is called the generalized affine scaling trajectory. By only assuming the existence of a finite optimal solution, we show that, starting from any interior feasible point, (i) the continuous trajectory is convergent; and (ii) the limit point is indeed an optimal solution of the original problem.
AB - In this paper, we propose and analyze a continuous trajectory, which is the solution of an ordinary differential equation (ODE) system for solving linearly constrained convex programming. The ODE system is formulated based on a first-order interior point method in [Math. Program., 127, 399–424 (2011)] which combines and extends a first-order affine scaling method and the replicator dynamics method for quadratic programming. The solution of the corresponding ODE system is called the generalized affine scaling trajectory. By only assuming the existence of a finite optimal solution, we show that, starting from any interior feasible point, (i) the continuous trajectory is convergent; and (ii) the limit point is indeed an optimal solution of the original problem.
KW - Continuous trajectory
KW - Convex programming
KW - Interior point method
KW - Ordinary differential equation
UR - http://www.scopus.com/inward/record.url?scp=85048058153&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-92537-0_17
DO - 10.1007/978-3-319-92537-0_17
M3 - Conference proceeding
AN - SCOPUS:85048058153
SN - 9783319925363
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 139
EP - 147
BT - Advances in Neural Networks - ISNN 2018 - 15th International Symposium on Neural Networks, ISNN 2018, Proceedings
A2 - Sun, Changyin
A2 - Tuzikov, Alexander V.
A2 - Huang, Tingwen
A2 - Lv, Jiancheng
PB - Springer Verlag
T2 - 15th International Symposium on Neural Networks, ISNN 2018
Y2 - 25 June 2018 through 28 June 2018
ER -