On the L1 exact penalty function with locally lipschitz functions

Liansheng Zhang; Zhijian Huang

doi:10.1007/BF02006063

On the L₁ exact penalty function with locally lipschitz functions

Liansheng Zhang^*, Zhijian Huang

^*Corresponding author for this work

Shanghai University

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we discuss the following inequality constrained optimization problem (P) min f(x) subject to g(x)≤0, g(x)=(g₁(x), ..., g_r(x))^τ, where f(x), g_j(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), ..., g_r(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).

Original language	English
Pages (from-to)	145-153
Number of pages	9
Journal	Acta Mathematicae Applicatae Sinica
Volume	4
Issue number	2
DOIs	https://doi.org/10.1007/BF02006063
Publication status	Published - May 1988
Externally published	Yes

Access to Document

10.1007/BF02006063

Cite this

@article{dddd86f7cedb4871ad1dac8db262da77,

title = "On the L1 exact penalty function with locally lipschitz functions",

abstract = "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).",

author = "Liansheng Zhang and Zhijian Huang",

year = "1988",

month = may,

doi = "10.1007/BF02006063",

language = "English",

volume = "4",

pages = "145--153",

journal = "Acta Mathematicae Applicatae Sinica",

issn = "0168-9673",

publisher = "Springer Verlag",

number = "2",

}

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 -

On the L₁ exact penalty function with locally lipschitz functions

Abstract

Access to Document

Other files and links

Fingerprint

Cite this