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

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Zhang, L., & Huang, Z. (1988). On the L₁ exact penalty function with locally lipschitz functions. Acta Mathematicae Applicatae Sinica, 4(2), 145-153. https://doi.org/10.1007/BF02006063

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On the L₁ exact penalty function with locally lipschitz functions

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