TY - JOUR
T1 - On the L1 exact penalty function with locally lipschitz functions
AU - Zhang, Liansheng
AU - Huang, Zhijian
PY - 1988/5
Y1 - 1988/5
N2 - In this paper, we discuss the following inequality constrained optimization problem (P) min f(x) subject to g(x)≤0, g(x)=(g1(x), ..., gr(x))τ, where f(x), gj(x)(j=1, ..., r) are locally Lipschitz functions. The L1 exact penalty function of the problem (P) is (PC) min f(x)+cp(x) subject to x εRn, where p(x)=max {0, g1(x), ..., gr(x)}, c>0. We will discuss the relationships between (P) and (PC). In particular, we will prove that under some (mild) conditions a local minimum of (PC) is also a local minimum of (P).
AB - In this paper, we discuss the following inequality constrained optimization problem (P) min f(x) subject to g(x)≤0, g(x)=(g1(x), ..., gr(x))τ, where f(x), gj(x)(j=1, ..., r) are locally Lipschitz functions. The L1 exact penalty function of the problem (P) is (PC) min f(x)+cp(x) subject to x εRn, where p(x)=max {0, g1(x), ..., gr(x)}, c>0. We will discuss the relationships between (P) and (PC). In particular, we will prove that under some (mild) conditions a local minimum of (PC) is also a local minimum of (P).
UR - http://www.scopus.com/inward/record.url?scp=34250087566&partnerID=8YFLogxK
U2 - 10.1007/BF02006063
DO - 10.1007/BF02006063
M3 - Article
AN - SCOPUS:34250087566
SN - 0168-9673
VL - 4
SP - 145
EP - 153
JO - Acta Mathematicae Applicatae Sinica
JF - Acta Mathematicae Applicatae Sinica
IS - 2
ER -