TY - JOUR
T1 - A continuous method for convex programming problems
AU - LIAO, Lizhi
N1 - Funding Information:
1This research was supported in part by Grants FRG/01-02/I-39 and FRG/01-02/II-06 of Hong Kong Baptist University and Grant HKBU2059/02P from the Research Grant Council of Hong Kong. 2The author thanks Professor Bingsheng He for many helpful suggestions and discussions. The author is also grateful for the comments and suggestions of two anonymous referees. In particular, the author is indebted to one referee who drew his attention to References 15, 17, 18. 3Associate Professor, Department of Mathematics, Hong Kong Baptist University, Hong Kong, PRC.
PY - 2005/1
Y1 - 2005/1
N2 - In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.
AB - In this paper, we present a continuous method for convex programming (CP) problems. Our approach converts first the convex problem into a monotone variational inequality (VI) problem. Then, a continuous method, which includes both a merit function and an ordinary differential equation (ODE), is introduced for the resulting variational inequality problem. The convergence of the ODE solution is proved for any starting point. There is no Lipschitz condition required in our proof. We show also that this limit point is an optimal solution for the original convex problem. Promising numerical results are presented.
KW - Continuous methods
KW - Convex programming
KW - Monotone variational inequalities
UR - http://www.scopus.com/inward/record.url?scp=13844275694&partnerID=8YFLogxK
U2 - 10.1007/s10957-004-6473-x
DO - 10.1007/s10957-004-6473-x
M3 - Journal article
AN - SCOPUS:13844275694
SN - 0022-3239
VL - 124
SP - 207
EP - 226
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
IS - 1
ER -