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

^*此作品的通讯作者

Shanghai University

科研成果: 期刊稿件 › 文章 › 同行评审

摘要

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).

源语言	英语
页（从-至）	145-153
页数	9
期刊	Acta Mathematicae Applicatae Sinica
卷	4
期	2
DOI	https://doi.org/10.1007/BF02006063
出版状态	已出版 - 5月 1988
已对外发布	是

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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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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).",

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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).

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JO - Acta Mathematicae Applicatae Sinica

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On the L1 exact penalty function with locally lipschitz functions

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On the L₁ exact penalty function with locally lipschitz functions