Abstract
In this paper, we discuss the following inequality constrained optimization problem (P) minf(x) subject tog(x)⩽0,g(x)=(g 1(x), ...,g r (x))τ, wheref(x),g j (x)(j=1, ...,r) are locally Lipschitz functions. TheL 1 exact penalty function of the problem (P) is (PC) minf(x)+cp(x) subject tox εR n, wherep(x)=max {0,g 1(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).
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Zhang, L., Huang, Z. On theL 1 exact penalty function with locally lipschitz functions. Acta Mathematicae Applicatae Sinica 4, 145–153 (1988). https://doi.org/10.1007/BF02006063
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DOI: https://doi.org/10.1007/BF02006063